Recent zbMATH articles in MSC 60https://www.zbmath.org/atom/cc/602021-04-16T16:22:00+00:00WerkzeugA stochastic evolutionary model for capturing human dynamics.https://www.zbmath.org/1456.911112021-04-16T16:22:00+00:00"Fenner, Trevor"https://www.zbmath.org/authors/?q=ai:fenner.trevor-i"Levene, Mark"https://www.zbmath.org/authors/?q=ai:levene.mark"Loizou, George"https://www.zbmath.org/authors/?q=ai:loizou.georgeVariational estimation of the drift for stochastic differential equations from the empirical density.https://www.zbmath.org/1456.620492021-04-16T16:22:00+00:00"Batz, Philipp"https://www.zbmath.org/authors/?q=ai:batz.philipp"Ruttor, Andreas"https://www.zbmath.org/authors/?q=ai:ruttor.andreas"Opper, Manfred"https://www.zbmath.org/authors/?q=ai:opper.manfredStability and hierarchy of quasi-stationary states: financial markets as an example.https://www.zbmath.org/1456.621152021-04-16T16:22:00+00:00"Stepanov, Yuriy"https://www.zbmath.org/authors/?q=ai:stepanov.yuriy"Rinn, Philip"https://www.zbmath.org/authors/?q=ai:rinn.philip"Guhr, Thomas"https://www.zbmath.org/authors/?q=ai:guhr.thomas"Peinke, Joachim"https://www.zbmath.org/authors/?q=ai:peinke.joachim"Schäfer, Rudi"https://www.zbmath.org/authors/?q=ai:schafer.rudiDistribution of complex algebraic numbers on the unit circle.https://www.zbmath.org/1456.111852021-04-16T16:22:00+00:00"Götze, F."https://www.zbmath.org/authors/?q=ai:gotze.friedrich-w"Gusakova, A."https://www.zbmath.org/authors/?q=ai:gusakova.anna"Kabluchko, Z."https://www.zbmath.org/authors/?q=ai:kabluchko.zakhar-a"Zaporozhets, D."https://www.zbmath.org/authors/?q=ai:zaporozhets.dmitrySummary: For \(- \pi \leq \beta_1 < \beta_2 \leq \pi \), denote by \(\Phi_{ \beta1,\beta 2}(Q)\) the amount of algebraic numbers of degree \(2m\), elliptic height at most \(Q\), and arguments in \([ \beta_1, \beta_2]\), lying on the unit circle. It is proved that
\[\Phi_{\beta_1,\beta_2}(Q)=Q^{m+1}\int_{\beta_1}^{\beta_2} p(t) dt+O\left(Q^m\log Q\right),\quad Q\to \infty,\]
where \(p(t)\) coincides up to a constant factor with density of the roots of a random trigonometrical polynomial. This density is calculated explicitly using the Edelman-Kostlan formula.Stochastic search with Poisson and deterministic resetting.https://www.zbmath.org/1456.602352021-04-16T16:22:00+00:00"Bhat, Uttam"https://www.zbmath.org/authors/?q=ai:bhat.uttam"De Bacco, Caterina"https://www.zbmath.org/authors/?q=ai:de-bacco.caterina"Redner, S."https://www.zbmath.org/authors/?q=ai:redner.sidneyTime fractional and space nonlocal stochastic Boussinesq equations driven by Gaussian white noise.https://www.zbmath.org/1456.370852021-04-16T16:22:00+00:00"Shen, Tianlong"https://www.zbmath.org/authors/?q=ai:shen.tianlong"Huang, Jianhua"https://www.zbmath.org/authors/?q=ai:huang.jianhua"Zeng, Caibin"https://www.zbmath.org/authors/?q=ai:zeng.caibinSummary: We present the time-spatial regularity of the nonlocal stochastic convolution for Caputo-type time fractional nonlocal Ornstein-Uhlenbeck equations, and establish the existence and uniqueness of mild solutions for time fractional and space nonlocal stochastic Boussinesq equations driven by Gaussian white noise.PATRICIA bridges.https://www.zbmath.org/1456.601812021-04-16T16:22:00+00:00"Evans, Steven N."https://www.zbmath.org/authors/?q=ai:evans.steven-neil"Wakolbinger, Anton"https://www.zbmath.org/authors/?q=ai:wakolbinger.antonEdge statistics for a class of repulsive particle systems.https://www.zbmath.org/1456.600222021-04-16T16:22:00+00:00"Kriecherbauer, Thomas"https://www.zbmath.org/authors/?q=ai:kriecherbauer.thomas"Venker, Martin"https://www.zbmath.org/authors/?q=ai:venker.martinSummary: We study a class of interacting particle systems on \(\mathbb {R}\) which was recently investigated by \textit{F. Götze} and \textit{M. Venker} [Ann. Probab. 42, No. 6, 2207--2242 (2014; Zbl 1301.60009)]. These ensembles generalize eigenvalue ensembles of Hermitian random matrices by allowing different interactions between particles. Although these ensembles are not known to be determinantal one can use the stochastic linearization method of Götze and Venker [loc. cit.] to represent them as averages of determinantal ones. Our results describe the transition between universal behavior in the regime of the Tracy-Widom law and non-universal behavior for large deviations of the rightmost particle. Moreover, a detailed analysis of the transition that occurs in the regime of moderate deviations, is provided. We also compare our results with the corresponding ones obtained recently for determinantal ensembles [\textit{P. Eichelsbacher} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 093, 18 p. (2016; Zbl 1348.60039); \textit{K. Schüler}, Moderate, large and superlarge deviations for extremal eigenvalues of unitarily invariant ensembles. Bayreuth: University of Bayreuth (PhD Thesis) (2015)]. In particular, we discuss how the averaging effects the leading order behavior in the regime of large deviations. In the analysis of the averaging procedure we use detailed asymptotic information on the behavior of Christoffel-Darboux kernels that is uniform for perturbative families of weights. Such results have been provided by \textit{K. Schubert}, \textit{K. Schüler} and the authors in [the first author et al., Markov Process. Relat. Fields 21, No. 3, 639--694 (2015; Zbl 1384.60025)].The genealogy of extremal particles of branching Brownian motion.https://www.zbmath.org/1456.602302021-04-16T16:22:00+00:00"Kliem, Sandra"https://www.zbmath.org/authors/?q=ai:kliem.sandra-m"Saha, Kumarjit"https://www.zbmath.org/authors/?q=ai:saha.kumarjitStochastic evolution of genealogies of spatial populations: state description, characterization of dynamics and properties.https://www.zbmath.org/1456.601802021-04-16T16:22:00+00:00"Depperschmidt, Andrej"https://www.zbmath.org/authors/?q=ai:depperschmidt.andrej"Greven, Andreas"https://www.zbmath.org/authors/?q=ai:greven.andreasExact probability distribution for the two-tag displacement in single-file motion.https://www.zbmath.org/1456.821802021-04-16T16:22:00+00:00"Sabhapandit, Sanjib"https://www.zbmath.org/authors/?q=ai:sabhapandit.sanjib"Dhar, Abhishek"https://www.zbmath.org/authors/?q=ai:dhar.abhishekThe SRPT service policy with frequency scaling: modeling, evaluation and optimization.https://www.zbmath.org/1456.602442021-04-16T16:22:00+00:00"Marin, Andrea"https://www.zbmath.org/authors/?q=ai:marin.andrea"Mitrani, Isi"https://www.zbmath.org/authors/?q=ai:mitrani.isi"Elahi, Maryam"https://www.zbmath.org/authors/?q=ai:elahi.maryam"Williamson, Carey"https://www.zbmath.org/authors/?q=ai:williamson.carey-lSummary: We study a system where the speed of a processor depends on the current number of jobs. A queuing model in which jobs consist of a variable number of tasks, and priority is given to the job with the fewest remaining tasks, is analyzed in the steady state. The number of processor frequency levels determines the dimensionality of the queuing process. The objective is to evaluate the trade-offs between holding costs and energy costs, when setting the processor frequency. We obtain exact results for two and three frequency levels, and accurate approximations that can be generalized further. Numerical and simulation experiments validate the approximations and provide insights into the benefits to be gained from optimizing the system.Generalized inverses of increasing functions and Lebesgue decomposition.https://www.zbmath.org/1456.600482021-04-16T16:22:00+00:00"de la Fortelle, Arnaud"https://www.zbmath.org/authors/?q=ai:de-la-fortelle.arnaudSummary: The reader should be aware of the explanatory nature of this article. Its main goal is to introduce to a broader vision of a topic than a more focused research paper, demonstrating some new results but mainly starting from some general consideration to build an overview of a theme with links to connected problems.
Our original question was related to the height of random growing trees. When investigating limit processes, we may consider some measures that are defined by increasing functions and their generalized inverses. And this leads to the analysis of Lebesgue decomposition of generalized inverses. Moreover, since the measures that motivated us initially are stochastic, there arises the idea of studying the continuity property of this transform in order to take limits.
When scaling growing processes like trees, time origin and scale can be replaced by another process. This leads us to a clock metaphor, to consider an increasing function as a clock reading from a given timeline. This is nothing more than an explanatory vision, not a mathematical concept, but this is the nature of this paper. So we consider an increasing function as a time change between two timelines; it leads to the idea that an increasing function and its generalized inverse play symmetric roles. We then introduce a universal time that links symmetrically an increasing function and its generalized inverse. We show how both are smoothly defined from this universal time. This allows to describe the Lebesgue decomposition for both an increasing function and its generalized inverse.Ergodicity of some dynamics of DNA sequences.https://www.zbmath.org/1456.601862021-04-16T16:22:00+00:00"Falconnet, Mikael"https://www.zbmath.org/authors/?q=ai:falconnet.mikael"Gantert, Nina"https://www.zbmath.org/authors/?q=ai:gantert.nina"Saada, Ellen"https://www.zbmath.org/authors/?q=ai:saada.ellenSummary: We define interacting particle systems on configurations of the integer lattice (with values in some finite alphabet) by the superimposition of two dynamics: a substitution process with finite range rates, and a circular permutation mechanism (called ``cut-and-paste'') with possibly unbounded range. The model is motivated by the dynamics of DNA sequences: we consider an ergodic model for substitutions, the RN+YpR model
[\textit{J. Bérard} et al., Math. Biosci. 211, No. 1, 56--88 (2008; Zbl 1130.92021)], with three particular cases, the models JC+cpg, T92+ccp, and RNc+YpR. We investigate whether they remain ergodic with the additional cut-and-paste mechanism, which models insertions and deletions of nucleotides. Using either duality or attractiveness techniques,
we provide various sets of sufficient conditions, concerning only the substitution rates, for ergodicity of the superimposed process. They imply ergodicity of the models JC+cpg, T92+cpg as well as the attractive RNc+YpR, all with an additional cut-and-paste mechanism.Networks with preferred degree: a mini-review and some new results.https://www.zbmath.org/1456.827242021-04-16T16:22:00+00:00"Bassler, Kevin E."https://www.zbmath.org/authors/?q=ai:bassler.kevin-e"Dhar, Deepak"https://www.zbmath.org/authors/?q=ai:dhar.deepak"Zia, R. K. P."https://www.zbmath.org/authors/?q=ai:zia.r-k-pNonequilibrium statistical mechanics of shear flow: invariant quantities and current relations.https://www.zbmath.org/1456.828612021-04-16T16:22:00+00:00"Baule, A."https://www.zbmath.org/authors/?q=ai:baule.adrian"Evans, R. M. L."https://www.zbmath.org/authors/?q=ai:evans.r-m-lSpatio-temporal dependence measures for bivariate AR(1) models with \(\alpha \)-stable noise.https://www.zbmath.org/1456.621902021-04-16T16:22:00+00:00"Grzesiek, Aleksandra"https://www.zbmath.org/authors/?q=ai:grzesiek.aleksandra"Sikora, Grzegorz"https://www.zbmath.org/authors/?q=ai:sikora.grzegorz"Teuerle, Marek"https://www.zbmath.org/authors/?q=ai:teuerle.marek-a"Wyłomańska, Agnieszka"https://www.zbmath.org/authors/?q=ai:wylomanska.agnieszkaThe authors investigate properties of the \(\alpha\)-stable bidimensional
vector autoregressive VAR(1) model described by the equation
\[
X (t) -\Theta X (t - 1) = Z (t) ,
\] where the noise \(\{Z (t)\}\)
is an \(\alpha\)-stable vector in \(\mathbb R^2\) with the stability index \(\alpha<2\)
called \(\alpha\)-stable noise (or an infinite-variance noise).
Under the condition that all the eigenvalues of the matrix \(\Theta\) are less than 1 in absolute value, which is equivalent to
\(\det(I - z\Theta)\not= 0\) for all \(\{z:|z|\leq 1\}\),
the defined by such an equation time series \(\{X (t)\}\) can be written in causal representation
\[
X(t) =\sum_{j=0}^{\infty}(\Theta)^jZ (t - j)
\]
In the case of (Gaussian) white noise \(\{Z (t)\}\) the spatio-temporal dependence structure of the bidimensional time series the cross-covariation is applied to describe properties of the time series. The cross-covariance has found many applications in time series investigation, especially in signal processing.
However, the cross-covariance is not an appropriate measure for the \(\alpha\)-stable stochastic processes where the second moment is infinite and therefore the theoretical function does not exist.
Then, for stochastic processes with infinite variance, the alternative measures should be applied.
In this article the authors propose the cross-codifference and the cross-covariation functions which are the analogues of the classical cross-covariance for infinite variance processes.
They provide theoretical results for cross-codifference and cross-covariation bidimensional VAR(1) time series with \(\alpha\)-stable i.i.d. noise and demonstrate that cross-codifference and cross-covariation can give different useful information about the relationships between components of bidimensional VAR models.
This article is an extension of the authors previous work (see [``Cross-codifference for bidimensional VAR(1) time series with infinite variance'', Comm. Stat. (to appear)]) where the cross-codifference was considered as the spatio-temporal measure of the components of VAR model based on sub-Gaussian distribution.
Reviewer: Mikhail P. Moklyachuk (Kyïv)Two-sample hypothesis testing for inhomogeneous random graphs.https://www.zbmath.org/1456.621082021-04-16T16:22:00+00:00"Ghoshdastidar, Debarghya"https://www.zbmath.org/authors/?q=ai:ghoshdastidar.debarghya"Gutzeit, Maurilio"https://www.zbmath.org/authors/?q=ai:gutzeit.maurilio"Carpentier, Alexandra"https://www.zbmath.org/authors/?q=ai:carpentier.alexandra"von Luxburg, Ulrike"https://www.zbmath.org/authors/?q=ai:von-luxburg.ulrikeTesting random graphs is challenging problem especially in large dimensions (chemical compounds graphs, brain networks of several patients analysis, and other). This paper focuses on the drawing inference from large sparse networks and consider the graphs on a common vertex set sampled from an inhomogeneous Erdös-Rényi model [\textit{B. Bollobàs} et al., Random Struct. Algorithms 31, No. 1, 3--122 (2007; Zbl 1123.05083)]. The latter model is considered in the case when no structural assumption on the population adjacency matrix is assumed.
Reviewer: Denis Sidorov (Irkutsk)Intermediate-level crossings of a first-passage path.https://www.zbmath.org/1456.602042021-04-16T16:22:00+00:00"Bhat, Uttam"https://www.zbmath.org/authors/?q=ai:bhat.uttam"Redner, S."https://www.zbmath.org/authors/?q=ai:redner.sidneyFractal transformed doubly reflected Brownian motions.https://www.zbmath.org/1456.602092021-04-16T16:22:00+00:00"Ehnes, Tim"https://www.zbmath.org/authors/?q=ai:ehnes.tim"Freiberg, Uta"https://www.zbmath.org/authors/?q=ai:freiberg.uta-renataOptimal strategy to capture a skittish Lamb wandering near a precipice.https://www.zbmath.org/1456.826532021-04-16T16:22:00+00:00"Chupeau, M."https://www.zbmath.org/authors/?q=ai:chupeau.marie"Bénichou, O."https://www.zbmath.org/authors/?q=ai:benichou.olivier"Redner, S."https://www.zbmath.org/authors/?q=ai:redner.sidneyInvariant sums of random matrices and the onset of level repulsion.https://www.zbmath.org/1456.820102021-04-16T16:22:00+00:00"Burda, Zdzisław"https://www.zbmath.org/authors/?q=ai:burda.zdzislaw"Livan, Giacomo"https://www.zbmath.org/authors/?q=ai:livan.giacomo"Vivo, Pierpaolo"https://www.zbmath.org/authors/?q=ai:vivo.pierpaoloExact formulas of the transition probabilities of the multi-species asymmetric simple exclusion process.https://www.zbmath.org/1456.826742021-04-16T16:22:00+00:00"Lee, Eunghyun"https://www.zbmath.org/authors/?q=ai:lee.eunghyunSummary: We find the formulas of the transition probabilities of the \(N\)-particle multi-species asymmetric simple exclusion processes (ASEP), and show that the transition probabilities are written as a determinant when the order of particles in the final state is the same as the order of particles in the initial state.Limit theorems for random simplices in high dimensions.https://www.zbmath.org/1456.520062021-04-16T16:22:00+00:00"Grote, Julian"https://www.zbmath.org/authors/?q=ai:grote.julian"Kabluchko, Zakhar"https://www.zbmath.org/authors/?q=ai:kabluchko.zakhar-a"Thäle, Christoph"https://www.zbmath.org/authors/?q=ai:thale.christophSummary: Let \(r=r(n)\) be a sequence of integers such that \(r\leq n\) and let \(X_1, \ldots, X_{r+1}\) be independent random points distributed according to the Gaussian, the Beta or the spherical distribution on \(\mathbb R^n\). Limit theorems for the log-volume and the volume of the random convex hull of \(X_1, \ldots, X_{r+1}\) are established in high dimensions, that is, as \(r\) and \(n\) tend to infinity simultaneously. This includes Berry-Esseen-type central limit theorems, log-normal limit theorems, and moderate and large deviations. Also different types of mod-\(\phi\) convergence are derived. The results heavily depend on the asymptotic growth of \(r\) relative to \(n\). For example, we prove that the fluctuations of the volume of the simplex are normal (respectively, log-normal) if \(r=o(n)\) (respectively, \(r\sim\alpha n\) for some \(0<\alpha<1\)).Power-law behaviors from the two-variable Langevin equation: Ito's and Stratonovich's Fokker-Planck equations.https://www.zbmath.org/1456.825572021-04-16T16:22:00+00:00"Guo, Ran"https://www.zbmath.org/authors/?q=ai:guo.ran"Du, Jiulin"https://www.zbmath.org/authors/?q=ai:du.jiulinConnectivity properties of the adjacency graph of \(\text{SLE}_{\kappa}\) bubbles for \(\kappa\in(4,8)\).https://www.zbmath.org/1456.602142021-04-16T16:22:00+00:00"Gwynne, Ewain"https://www.zbmath.org/authors/?q=ai:gwynne.ewain"Pfeffer, Joshua"https://www.zbmath.org/authors/?q=ai:pfeffer.joshuaSummary: We study the adjacency graph of bubbles, that is, complementary connected components of a \(\text{SLE}_{\kappa}\) curve for \(\kappa\in (4,8)\), with two such bubbles considered to be adjacent if their boundaries intersect. We show that this adjacency graph is a.s. connected for \(\kappa\in (4,\kappa_0]\), where \(\kappa_0\approx 5.6158\) is defined explicitly. This gives a partial answer to a problem posed by \textit{B. Duplantier} et al. [``Liouville quantum gravity as a mating of trees'', Preprint, \url{arXiv:1409.7055}]. Our proof in fact yields a stronger connectivity result for \(\kappa\in (4,\kappa_0]\), which says that there is a Markovian way of finding a path from any fixed bubble to \(\infty \). We also show that there is a (nonexplicit) \(\kappa_1\in (\kappa_0,8)\) such that this stronger condition does not hold for \(\kappa\in [\kappa_1,8)\).
Our proofs are based on an encoding of \(\text{SLE}_{\kappa}\) in terms of a pair of independent \(\kappa/4\)-stable processes, which allows us to reduce our problem to a problem about stable processes. In fact, due to this encoding, our results can be rephrased as statements about the connectivity of the adjacency graph of loops when one glues together an independent pair of so-called \(\kappa/4\)-stable looptrees, as studied, for example, by \textit{N. Curien} and \textit{I. Kortchemski} [Electron. J. Probab. 19, Paper No. 108, 35 p. (2014; Zbl 1307.60061)]
The above encoding comes from the theory of Liouville quantum gravity (LQG), but the paper can be read without any knowledge of LQG if one takes the encoding as a black box.Sparse approximation based on a random overcomplete basis.https://www.zbmath.org/1456.620142021-04-16T16:22:00+00:00"Nakanishi-Ohno, Yoshinori"https://www.zbmath.org/authors/?q=ai:nakanishi-ohno.yoshinori"Obuchi, Tomoyuki"https://www.zbmath.org/authors/?q=ai:obuchi.tomoyuki"Okada, Masato"https://www.zbmath.org/authors/?q=ai:okada.masato"Kabashima, Yoshiyuki"https://www.zbmath.org/authors/?q=ai:kabashima.yoshiyukiNoise-induced phenomena in the dynamics of groundwater-dependent plant ecosystems with time delay.https://www.zbmath.org/1456.921502021-04-16T16:22:00+00:00"Jia, Zheng-Lin"https://www.zbmath.org/authors/?q=ai:jia.zhenglin"Mei, Dong-Cheng"https://www.zbmath.org/authors/?q=ai:mei.dongchengMulti-condition of stability for nonlinear stochastic non-autonomous delay differential equation.https://www.zbmath.org/1456.340782021-04-16T16:22:00+00:00"Shaikhet, Leonid"https://www.zbmath.org/authors/?q=ai:shaikhet.leonid-eSummary: A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for exponential mean square stability of the linear part of the considered nonlinear equation also are sufficient conditions for stability in probability of the initial nonlinear equation. Some new sufficient condition of stability in probability for the zero solution of the considered nonlinear non-autonomous stochastic differential equation is obtained which can be considered as a multi-condition of stability because it allows to get for one considered equation at once several different complementary of each other sufficient stability conditions. The obtained results are illustrated with numerical simulations and figures.Entropic repulsion for the occupation-time field of random interlacements conditioned on disconnection.https://www.zbmath.org/1456.601892021-04-16T16:22:00+00:00"Chiarini, Alberto"https://www.zbmath.org/authors/?q=ai:chiarini.alberto"Nitzschner, Maximilian"https://www.zbmath.org/authors/?q=ai:nitzschner.maximilianSummary: We investigate percolation of the vacant set of random interlacements on \(\mathbb{Z}^d,d\geq 3\), in the strongly percolative regime. We consider the event that the interlacement set at level \(u\) disconnects the discrete blow-up of a compact set \(A\subseteq\mathbb{R}^d\) from the boundary of an enclosing box. We derive asymptotic large deviation upper bounds on the probability that the local averages of the occupation times deviate from a specific function depending on the harmonic potential of \(A\), when disconnection occurs. If certain critical levels coincide, which is plausible but open at the moment, these bounds imply that conditionally on disconnection, the occupation-time profile undergoes an entropic push governed by a specific function depending on \(A\). Similar entropic repulsion phenomena conditioned on disconnection by level-sets of the discrete Gaussian free field on \(\mathbb{Z}^d,d\geq 3\), have been obtained by the authors in [Probab. Theory Relat. Fields 177, No. 1--2, 525--575 (2020; Zbl 07202717)]. Our proofs rely crucially on the ``solidification estimates'' developed in [the second author and \textit{A.-S. Sznitman}, J. Eur. Math. Soc. (JEMS) 22, No. 8, 2629--2672 (2020; Zbl 07227743)].Markovian dynamics of exchangeable arrays.https://www.zbmath.org/1456.600762021-04-16T16:22:00+00:00"Černý, Jiří"https://www.zbmath.org/authors/?q=ai:cerny.jiri"Klimovsky, Anton"https://www.zbmath.org/authors/?q=ai:klimovsky.antonAn exponential bound for Cox regression.https://www.zbmath.org/1456.622342021-04-16T16:22:00+00:00"Goldberg, Y."https://www.zbmath.org/authors/?q=ai:goldberg.yair"Kosorok, M. R."https://www.zbmath.org/authors/?q=ai:kosorok.michael-rSummary: We present an asymptotic exponential bound for the deviation of the survival function estimator of the Cox model. We show that the bound holds even when the proportional hazards assumption does not hold.Towards an information-theoretic model of the Allison mixture stochastic process.https://www.zbmath.org/1456.620132021-04-16T16:22:00+00:00"Gunn, Lachlan J."https://www.zbmath.org/authors/?q=ai:gunn.lachlan-j"Chapeau-Blondeau, François"https://www.zbmath.org/authors/?q=ai:chapeau-blondeau.francois"Allison, Andrew"https://www.zbmath.org/authors/?q=ai:allison.andrew-gordon"Abbott, Derek"https://www.zbmath.org/authors/?q=ai:abbott.derekBayesian model selection with fractional Brownian motion.https://www.zbmath.org/1456.620442021-04-16T16:22:00+00:00"Krog, Jens"https://www.zbmath.org/authors/?q=ai:krog.jens"Jacobsen, Lars H."https://www.zbmath.org/authors/?q=ai:jacobsen.lars-h"Lund, Frederik W."https://www.zbmath.org/authors/?q=ai:lund.frederik-w"Wüstner, Daniel"https://www.zbmath.org/authors/?q=ai:wustner.daniel"Lomholt, Michael A."https://www.zbmath.org/authors/?q=ai:lomholt.michael-aProbabilistic characteristics of noisy Van der Pol type oscillator with nonlinear damping.https://www.zbmath.org/1456.340322021-04-16T16:22:00+00:00"Dubkov, A. A."https://www.zbmath.org/authors/?q=ai:dubkov.alexander-a"Litovsky, I. A."https://www.zbmath.org/authors/?q=ai:litovsky.i-aModeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations.https://www.zbmath.org/1456.601502021-04-16T16:22:00+00:00"Kaulakys, B."https://www.zbmath.org/authors/?q=ai:kaulakys.b"Alaburda, M."https://www.zbmath.org/authors/?q=ai:alaburda.m"Ruseckas, J."https://www.zbmath.org/authors/?q=ai:ruseckas.juliusAlgebraic and arithmetic area for \(m\) planar Brownian paths.https://www.zbmath.org/1456.602072021-04-16T16:22:00+00:00"Desbois, Jean"https://www.zbmath.org/authors/?q=ai:desbois.jean"Ouvry, Stéphane"https://www.zbmath.org/authors/?q=ai:ouvry.stephaneBoundary behavior of random walks in cones.https://www.zbmath.org/1456.601102021-04-16T16:22:00+00:00"Raschel, Kilian"https://www.zbmath.org/authors/?q=ai:raschel.kilian"Tarrago, Pierre"https://www.zbmath.org/authors/?q=ai:tarrago.pierreSummary: We study the asymptotic behavior of zero-drift random walks confined to multidimensional convex cones, when the endpoint is close to the boundary. We derive a local limit theorem in the fluctuation regime.Poker as a skill game: rational versus irrational behaviors.https://www.zbmath.org/1456.910332021-04-16T16:22:00+00:00"Javarone, Marco Alberto"https://www.zbmath.org/authors/?q=ai:javarone.marco-albertoBreakdown of the finite-time and -population scalings of the large deviation function in the large-size limit of a contact process.https://www.zbmath.org/1456.600062021-04-16T16:22:00+00:00"Guevara Hidalgo, Esteban"https://www.zbmath.org/authors/?q=ai:hidalgo.esteban-guevaraApplication of Markov chains in managing human potentials.https://www.zbmath.org/1456.601822021-04-16T16:22:00+00:00"Hrustek, Nikolina Žajdela"https://www.zbmath.org/authors/?q=ai:hrustek.nikolina-zajdela"Keček, Damira"https://www.zbmath.org/authors/?q=ai:kecek.damira"Polgar, Ines"https://www.zbmath.org/authors/?q=ai:polgar.inesSummary: Human potentials make a unique foundation to every organization. Due to individuals' differences which enable a business surroundings and create competitive advantage, it is necessary to coordinate them to the mission, vision and goals set by the organization in order to satisfy the needs for specific knowledge and skills, and effectively realize the defined business goals. Application of Markov chains enables prediction of random variables' movements. This study shows, via a practical example, predicting the necessity for human potentials in an ICT company throughout a period of three years.On the relationship between Gaussian stochastic blockmodels and label propagation algorithms.https://www.zbmath.org/1456.681712021-04-16T16:22:00+00:00"Zhang, Junhao"https://www.zbmath.org/authors/?q=ai:zhang.junhao"Chen, Tongfei"https://www.zbmath.org/authors/?q=ai:chen.tongfei"Hu, Junfeng"https://www.zbmath.org/authors/?q=ai:hu.junfengOn impatience in Markovian \(M/M/1/N/DWV\) queue with vacation interruption.https://www.zbmath.org/1456.900532021-04-16T16:22:00+00:00"Bouchentouf, Amina Angelika"https://www.zbmath.org/authors/?q=ai:bouchentouf.amina-angelika"Guendouzi, Abdelhak"https://www.zbmath.org/authors/?q=ai:guendouzi.abdelhak"Majid, Shakir"https://www.zbmath.org/authors/?q=ai:majid.shakirSummary: The aim of this paper is to establish a cost optimization analysis for an \(M/M/1/N\) queuing system with differentiated working vacations, Bernoulli schedule vacation interruption, balking and reneging. Once the system is empty, the server waits a random amount of time before he goes on working vacation during which service is provided with a lower rate. At the instant of the service achievement in the vacation period, if there are customers in the system at that time, the vacation is interrupted and the server returns to the regular busy period with probability \(\beta'\) or continues the vacation with probability \(1 - \beta'\). Once the working vacation is ended. The server returns to the normal busy period. If there are still no customers in the system, the server can take another working vacation of shorter duration. During working vacation periods, arriving customers become impatient with an individual timer which is exponentially distributed. Explicit expressions for the steady-state system size probabilities are derived using recursive technique. Further, interesting performance measures are explicitly obtained. Then, we construct a cost model in order to determine the optimal values of service rates, simultaneously, to minimize the total expected cost per unit time by using a quadratic fit search method (QFSM). Finally, numerical illustrations are added to validate the theoretical results.Competition and evolution in restricted space.https://www.zbmath.org/1456.921152021-04-16T16:22:00+00:00"Forgerini, F. L."https://www.zbmath.org/authors/?q=ai:forgerini.fabricio-l"Crokidakis, N."https://www.zbmath.org/authors/?q=ai:crokidakis.nunoFluctuations in interacting particle systems with memory.https://www.zbmath.org/1456.826612021-04-16T16:22:00+00:00"Harris, Rosemary J."https://www.zbmath.org/authors/?q=ai:harris.rosemary-jOccupation times for single-file diffusion.https://www.zbmath.org/1456.826482021-04-16T16:22:00+00:00"Bénichou, Olivier"https://www.zbmath.org/authors/?q=ai:benichou.olivier"Desbois, Jean"https://www.zbmath.org/authors/?q=ai:desbois.jeanA note on stationary bootstrap variance estimator under long-range dependence.https://www.zbmath.org/1456.620472021-04-16T16:22:00+00:00"Kang, Taegyu"https://www.zbmath.org/authors/?q=ai:kang.taegyu"Kim, Young Min"https://www.zbmath.org/authors/?q=ai:kim.youngmin"Im, Jongho"https://www.zbmath.org/authors/?q=ai:im.jonghoSummary: The stationary bootstrap method is popularly used to compute the standard errors or confidence regions of estimators, generated from time processes exhibiting weakly dependent stationarity. Most previous stationary bootstrap methods have focused on studying large-sample properties of stationary bootstrap inference about a sample mean under short-range dependence. For long-range dependence, recent studies have investigated the properties of block bootstrap methods using overlapping and non-overlapping blocking techniques with fixed block lengths. However, the characteristics of a stationary bootstrap with random block lengths are less well-known under long-range dependence. We investigate the asymptotic property of a stationary bootstrap variance estimator for a sample mean under long-range dependence. Our theoretical and simulation results indicate that the stationary bootstrap method does not have \(\sqrt{ n} \)-consistency for stationary and long-range dependent time processes.Exclusion in a priority queue.https://www.zbmath.org/1456.900552021-04-16T16:22:00+00:00"de Gier, Jan"https://www.zbmath.org/authors/?q=ai:de-gier.jan"Finn, Caley"https://www.zbmath.org/authors/?q=ai:finn.caleyStochastic acceleration in generalized squared Bessel processes.https://www.zbmath.org/1456.601692021-04-16T16:22:00+00:00"Valenti, D."https://www.zbmath.org/authors/?q=ai:valenti.davide"Chichigina, O. A."https://www.zbmath.org/authors/?q=ai:chichigina.olga-a"Dubkov, A. A."https://www.zbmath.org/authors/?q=ai:dubkov.alexander-a"Spagnolo, B."https://www.zbmath.org/authors/?q=ai:spagnolo.bernardoNonparametric detection of change in the slope and intercept in linear structural errors-in-variables models.https://www.zbmath.org/1456.620872021-04-16T16:22:00+00:00"Martsynyuk, Yuliya V."https://www.zbmath.org/authors/?q=ai:martsynyuk.yuliya-vSummary: This paper deals with two generalizations of the classical linear structural errors-in-variables model (SEIVM) with univariate observations. In these two models, the data may no longer come from a single linear SEIVM, due to that a change in the slope in the first model and a change in the intercept in the second model may occur after observing the first \(k^\ast\) data pairs, where \(k^\ast\) is assumed to be unknown, while the explanatory variables as well as vectors of the measurement errors are independent and identically distributed. \textit{Nonparametric} asymptotic tests are developed to detect a possible change in each of these SEIVM's, assuming the existence of four moments for the explanatory and error variables. It appears that the SEIVM with a possible change in the slope of this paper has not been considered in the literature, while the SEIVM with a possible change in the intercept has not been studied before \textit{nonparametrically}.Note on a q-modified central limit theorem.https://www.zbmath.org/1456.600602021-04-16T16:22:00+00:00"Hilhorst, H. J."https://www.zbmath.org/authors/?q=ai:hilhorst.hendrik-janNetwork evolution induced by the dynamical rules of two populations.https://www.zbmath.org/1456.921242021-04-16T16:22:00+00:00"Platini, Thierry"https://www.zbmath.org/authors/?q=ai:platini.thierry"Zia, R. K. P."https://www.zbmath.org/authors/?q=ai:zia.r-k-pAn equal-time correlation function for directed percolation.https://www.zbmath.org/1456.828392021-04-16T16:22:00+00:00"Beljakov, I."https://www.zbmath.org/authors/?q=ai:belyakov.i-m|belyakov.i-v"Hinrichsen, H."https://www.zbmath.org/authors/?q=ai:hinrichsen.haye|hinrichsen.holgerFrom interacting particle systems to random matrices.https://www.zbmath.org/1456.826572021-04-16T16:22:00+00:00"Ferrari, Patrik L."https://www.zbmath.org/authors/?q=ai:ferrari.patrik-linoAsymmetric simple exclusion process on a Cayley tree.https://www.zbmath.org/1456.826472021-04-16T16:22:00+00:00"Basu, Mahashweta"https://www.zbmath.org/authors/?q=ai:basu.mahashweta"Mohanty, P. K."https://www.zbmath.org/authors/?q=ai:mohanty.prasanta-kumarRecords and sequences of records from random variables with a linear trend.https://www.zbmath.org/1456.601252021-04-16T16:22:00+00:00"Franke, Jasper"https://www.zbmath.org/authors/?q=ai:franke.jasper"Wergen, Gregor"https://www.zbmath.org/authors/?q=ai:wergen.gregor"Krug, Joachim"https://www.zbmath.org/authors/?q=ai:krug.joachimContinuous-time ballistic process with random resets.https://www.zbmath.org/1456.600752021-04-16T16:22:00+00:00"Villarroel, Javier"https://www.zbmath.org/authors/?q=ai:villarroel.javier"Montero, Miquel"https://www.zbmath.org/authors/?q=ai:montero.miquelConstructing analytically tractable ensembles of stochastic covariances with an application to financial data.https://www.zbmath.org/1456.600232021-04-16T16:22:00+00:00"Meudt, Frederik"https://www.zbmath.org/authors/?q=ai:meudt.frederik"Theissen, Martin"https://www.zbmath.org/authors/?q=ai:theissen.martin"Schäfer, Rudi"https://www.zbmath.org/authors/?q=ai:schafer.rudi"Guhr, Thomas"https://www.zbmath.org/authors/?q=ai:guhr.thomasOn the sub-gaussianity of the \(r\)-correlograms.https://www.zbmath.org/1456.600802021-04-16T16:22:00+00:00"Giuliano, R."https://www.zbmath.org/authors/?q=ai:giuliano.rita"Cabrera, M. Ordóñez"https://www.zbmath.org/authors/?q=ai:ordonez-cabrera.manuel-h"Volodin, A."https://www.zbmath.org/authors/?q=ai:volodin.andrej-i|volodin.andrei-iLarge deviations of spread measures for Gaussian matrices.https://www.zbmath.org/1456.600172021-04-16T16:22:00+00:00"Cunden, Fabio Deelan"https://www.zbmath.org/authors/?q=ai:cunden.fabio-deelan"Vivo, Pierpaolo"https://www.zbmath.org/authors/?q=ai:vivo.pierpaoloASEP on a ring conditioned on enhanced flux.https://www.zbmath.org/1456.823092021-04-16T16:22:00+00:00"Popkov, Vladislav"https://www.zbmath.org/authors/?q=ai:popkov.vladislav"Schütz, Gunter M."https://www.zbmath.org/authors/?q=ai:schutz.gunter-m"Simon, Damien"https://www.zbmath.org/authors/?q=ai:simon.damienLimit theorems for record indicators in threshold \(F^\alpha \)-schemes.https://www.zbmath.org/1456.600692021-04-16T16:22:00+00:00"He, P."https://www.zbmath.org/authors/?q=ai:he.puyu|he.pimo|he.pinjie|he.peiyu|he.peiren|he.pingan|he.pengfei|he.peiling|he.paul|he.puyan|he.pei|he.peijie|he.pengcai|he.peilun|he.peng|he.ping|he.peijun|he.peiying|he.peixiang|he.peipei|he.pingfan|he.pu|he.peisong|he.peter|he.peixing|he.peikun|he.pilian|he.pengzhang|he.puhan|he.penghui"Borovkov, K. A."https://www.zbmath.org/authors/?q=ai:borovkov.konstantin-aOn the times of attaining high levels by a random walk in a random environment.https://www.zbmath.org/1456.602682021-04-16T16:22:00+00:00"Afanasyev, V. I."https://www.zbmath.org/authors/?q=ai:afanasev.valerii-ivanovichScalings and fractals in information geometry: Ornstein-Uhlenbeck processes.https://www.zbmath.org/1456.601282021-04-16T16:22:00+00:00"Oxley, William"https://www.zbmath.org/authors/?q=ai:oxley.william"Kim, Eun-Jin"https://www.zbmath.org/authors/?q=ai:kim.eunjinResponse behavior of aging systems with temporal disorder.https://www.zbmath.org/1456.602732021-04-16T16:22:00+00:00"Eule, Stephan"https://www.zbmath.org/authors/?q=ai:eule.stephanCorrelation functions in conformal invariant stochastic processes.https://www.zbmath.org/1456.602322021-04-16T16:22:00+00:00"Alcaraz, Francisco C."https://www.zbmath.org/authors/?q=ai:alcaraz.francisco-castilho"Rittenberg, Vladimir"https://www.zbmath.org/authors/?q=ai:rittenberg.vladimirRemarks on the nonlocal Dirichlet problem.https://www.zbmath.org/1456.350592021-04-16T16:22:00+00:00"Grzywny, Tomasz"https://www.zbmath.org/authors/?q=ai:grzywny.tomasz"Kassmann, Moritz"https://www.zbmath.org/authors/?q=ai:kassmann.moritz"Leżaj, Łukasz"https://www.zbmath.org/authors/?q=ai:lezaj.lukaszSummary: We study translation-invariant integrodifferential operators that generate Lévy processes. First, we investigate different notions of what a solution to a nonlocal Dirichlet problem is and we provide the classical representation formula for distributional solutions. Second, we study the question under which assumptions distributional solutions are twice differentiable in the classical sense. Sufficient conditions and counterexamples are provided.Extreme value statistics from the real space renormalization group: Brownian motion, Bessel processes and continuous time random walks.https://www.zbmath.org/1456.824052021-04-16T16:22:00+00:00"Schehr, Grégory"https://www.zbmath.org/authors/?q=ai:schehr.gregory"Le Doussal, Pierre"https://www.zbmath.org/authors/?q=ai:le-doussal.pierreAnalysis of MAP/PH(1), PH(2)/2 queue with Bernoulli schedule vacation, Bernoulli feedback and renege of customers.https://www.zbmath.org/1456.602372021-04-16T16:22:00+00:00"Ayyappan, G."https://www.zbmath.org/authors/?q=ai:ayyappan.govindasamy"Gowthami, R."https://www.zbmath.org/authors/?q=ai:gowthami.rSummary: A classical queueing model with two servers in which the inter arrival times follow Markovian arrival process, the service times are phase type distributed and the remaining random variables are exponentially distributed is studied in this paper. The resulting QBD process is investigated in the steady state by employing matrix-analytic method. We have also done the busy period analysis of our model and discussed about the waiting time distribution for our system. Some of the performance measures are provided. Finally, a few numerical and graphical examples are given.Diffusion maps tailored to arbitrary non-degenerate Itô processes.https://www.zbmath.org/1456.601982021-04-16T16:22:00+00:00"Banisch, Ralf"https://www.zbmath.org/authors/?q=ai:banisch.ralf"Trstanova, Zofia"https://www.zbmath.org/authors/?q=ai:trstanova.zofia"Bittracher, Andreas"https://www.zbmath.org/authors/?q=ai:bittracher.andreas"Klus, Stefan"https://www.zbmath.org/authors/?q=ai:klus.stefan"Koltai, Péter"https://www.zbmath.org/authors/?q=ai:koltai.peterSummary: We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling density, with the gradient of an arbitrary density of interest which is known up to a normalization constant. The second generalization allows for a diffusion map type approximation of the forward and backward generators of general Itô diffusions with given drift and diffusion coefficients. We use the local kernels introduced by \textit{T. Berry} and \textit{T. Sauer} [Appl. Comput. Harmon. Anal. 40, No. 3, 439--469 (2016; Zbl 1376.94002)], but allow for arbitrary sampling densities. We provide numerical illustrations to demonstrate that this opens up many new applications for diffusion maps as a tool to organize point cloud data, including biased or corrupted samples, dimension reduction for dynamical systems, detection of almost invariant regions in flow fields, and importance sampling.A generalized Fourier transform approach to risk measures.https://www.zbmath.org/1456.911282021-04-16T16:22:00+00:00"Bormetti, Giacomo"https://www.zbmath.org/authors/?q=ai:bormetti.giacomo"Cazzola, Valentina"https://www.zbmath.org/authors/?q=ai:cazzola.valentina"Livan, Giacomo"https://www.zbmath.org/authors/?q=ai:livan.giacomo"Montagna, Guido"https://www.zbmath.org/authors/?q=ai:montagna.guido"Nicrosini, Oreste"https://www.zbmath.org/authors/?q=ai:nicrosini.oresteTime-inhomogeneous random Markov chains.https://www.zbmath.org/1456.601782021-04-16T16:22:00+00:00"Innocentini, G. C. P."https://www.zbmath.org/authors/?q=ai:innocentini.guilherme-c-p"Novaes, M."https://www.zbmath.org/authors/?q=ai:novaes.marcel|novaes.marcosMinimax rates for the covariance estimation of multi-dimensional Lévy processes with high-frequency data.https://www.zbmath.org/1456.601162021-04-16T16:22:00+00:00"Papagiannouli, Katerina"https://www.zbmath.org/authors/?q=ai:papagiannouli.katerinaSummary: This article studies nonparametric methods to estimate the co-integrated volatility of multi-dimensional Lévy processes with high frequency data. We construct a spectral estimator for the co-integrated volatility and prove minimax rates for an appropriate bounded nonparametric class of Lévy processes. Given \(n\) observations of increments over intervals of length \(1/n\), the rates of convergence are \(1/\sqrt{n}\) if \(r\leq 1\) and \((n\log n)^{(r-2)/2}\) if \(r>1\), where \(r\) is the co-jump activity index and corresponds to the intensity of dependent jumps. These rates are optimal in a minimax sense. We bound the co-jump activity index from below by the harmonic mean of the jump activity indices of the components. Finally, we assess the efficiency of our estimator by comparing it with estimators in the existing literature.Convergence in Monge-Wasserstein distance of mean field systems with locally Lipschitz coefficients.https://www.zbmath.org/1456.600722021-04-16T16:22:00+00:00"Dung Tien Nguyen"https://www.zbmath.org/authors/?q=ai:dung-tien-nguyen."Son Luu Nguyen"https://www.zbmath.org/authors/?q=ai:son-luu-nguyen."Nguyen Huu Du"https://www.zbmath.org/authors/?q=ai:nguyen-huu-du.Summary: This paper focuses on stochastic systems of weakly interacting particles whose dynamics depend on the empirical measures of the whole populations. The drift and diffusion coefficients of the dynamical systems are assumed to be locally Lipschitz continuous and satisfy global linear growth condition. The limits of such systems as the number of particles tends to infinity are studied, and the rate of convergence of the sequences of empirical measures to their limits in terms of \(p^{\text{th}}\) Monge-Wasserstein distance is established. We also investigate the existence, uniqueness, and boundedness, and continuity of solutions of the limiting McKean-Vlasov equations associated to the systems.Convex bound approximations for sums of random variables under multivariate log-generalized hyperbolic distribution and asymptotic equivalences.https://www.zbmath.org/1456.600572021-04-16T16:22:00+00:00"Li, Zihao"https://www.zbmath.org/authors/?q=ai:li.zihao"Luo, Ji"https://www.zbmath.org/authors/?q=ai:luo.ji"Yao, Jing"https://www.zbmath.org/authors/?q=ai:yao.jingSummary: We propose convex bound approximations for the sum of log-multivariate generalized hyperbolic random variables. We derive explicit formulas for the distributions of convex bounds and for the frequently-used risk measures such as Value-at-Risk, Conditional Tail Expectation and stop-loss premium. We present numerical results showing that such approximations are not only accurate but also robust. Moreover, we further prove that there exist asymptotic equivalences between the sum and its convex bounds. To further illustrate the potentials of the convex bound approximations, we provide an application to capital allocation. We show that our formulas can be easily applied to precisely approximate capital allocation rule based on the conditional tail expectation.Modeling the coupled return-spread high frequency dynamics of large tick assets.https://www.zbmath.org/1456.911312021-04-16T16:22:00+00:00"Curato, Gianbiagio"https://www.zbmath.org/authors/?q=ai:curato.gianbiagio"Lillo, Fabrizio"https://www.zbmath.org/authors/?q=ai:lillo.fabrizioIrreversible blocking in single-file concurrent and countercurrent particulate flows.https://www.zbmath.org/1456.826962021-04-16T16:22:00+00:00"Talbot, J."https://www.zbmath.org/authors/?q=ai:talbot.julian"Gabrielli, A."https://www.zbmath.org/authors/?q=ai:gabrielli.alessandro|gabrielli.andrea"Viot, P."https://www.zbmath.org/authors/?q=ai:viot.pascalError analysis of the Wiener-Askey polynomial chaos with hyperbolic cross approximation and its application to differential equations with random input.https://www.zbmath.org/1456.651732021-04-16T16:22:00+00:00"Luo, Xue"https://www.zbmath.org/authors/?q=ai:luo.xueSummary: It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the ``curse of dimensionality'' in some degree. In this note, we give the error estimate of hyperbolic cross (HC) approximations with all sorts of Askey polynomials. These polynomials are useful in generalized polynomial chaos (gPC) in the field of uncertainty quantification. The exponential convergences in both regular and optimized HC approximations have been shown under the condition that the random variable depends on the random inputs smoothly in some degree. Moreover, we apply gPC to numerically solve the ordinary differential equations with slightly higher dimensional random inputs. Both regular and optimized HC have been investigated with Laguerre-chaos, Charlier-chaos and Hermite-chaos in the numerical experiment. The discussion of the connection between the standard ANOVA approximation and Galerkin approximation is in the appendix.Thermodynamic limits to information harvesting by sensory systems.https://www.zbmath.org/1456.940262021-04-16T16:22:00+00:00"Bo, Stefano"https://www.zbmath.org/authors/?q=ai:bo.stefano"Del Giudice, Marco"https://www.zbmath.org/authors/?q=ai:giudice.marco-del"Celani, Antonio"https://www.zbmath.org/authors/?q=ai:celani.antonioThe statistics of fixation times for systems with recruitment.https://www.zbmath.org/1456.623132021-04-16T16:22:00+00:00"Biancalani, Tommaso"https://www.zbmath.org/authors/?q=ai:biancalani.tommaso"Dyson, Louise"https://www.zbmath.org/authors/?q=ai:dyson.louise"McKane, Alan J."https://www.zbmath.org/authors/?q=ai:mckane.alan-jAsymmetric exclusion processes on a closed network with bottlenecks.https://www.zbmath.org/1456.828622021-04-16T16:22:00+00:00"Chatterjee, Rakesh"https://www.zbmath.org/authors/?q=ai:chatterjee.rakesh"Chandra, Anjan Kumar"https://www.zbmath.org/authors/?q=ai:chandra.anjan-kumar"Basu, Abhik"https://www.zbmath.org/authors/?q=ai:basu.abhikMutant number distribution in an exponentially growing population.https://www.zbmath.org/1456.920502021-04-16T16:22:00+00:00"Keller, Peter"https://www.zbmath.org/authors/?q=ai:keller.peter-e"Antal, Tibor"https://www.zbmath.org/authors/?q=ai:antal.tiborDynamics for spherical spin glasses: disorder dependent initial conditions.https://www.zbmath.org/1456.828462021-04-16T16:22:00+00:00"Dembo, Amir"https://www.zbmath.org/authors/?q=ai:dembo.amir"Subag, Eliran"https://www.zbmath.org/authors/?q=ai:subag.eliranIn the paper the authors investigated the thermodynamic (\(N\to\infty\)), long-time (\(t\to\infty\)), behavior of a class of systems composed of \(N\) Langevin particles interacting with each other through a random potential.
Namely, the thermodynamic limit of the empirical correlation and response functions is derived for spherical mixed p-spin disordered mean-field models, starting uniformly within one of the spherical bands on which (at low temperature) the Gibbs measure concentrates for the pure p-spin models and mixed perturbations of them. Moreover, the large time asymptotics of the corresponding coupled non-linear integro-differential equations is related to the geometric structure of the Gibbs measures (at low temperature), and derive their FDT (Fluctuation Dissipation Theorem) solution (at high temperature).
Reviewer: Utkir A. Rozikov (Tashkent)On volume and surface densities of dynamical germ-grain models with ellipsoidal growth: a rigorous approach with applications to materials science.https://www.zbmath.org/1456.600452021-04-16T16:22:00+00:00"Villa, Elena"https://www.zbmath.org/authors/?q=ai:villa.elena"Rios, Paulo R."https://www.zbmath.org/authors/?q=ai:rios.paulo-rSummary: Many engineering materials of interest are polycrystals: an aggregate of many crystals with size usually below \(100\mu\)m. Those small crystals are called the grains of the polycrystal, and are often equiaxed. However, because of processing, the grain shape may become anisotropic; for instance, during recrystallization or phase transformations, the new grains may grow in the form of ellipsoids. Heavily anisotropic grains may result from a process, such as rolling, and they may have most of their interfacial area parallel to the rolling plane. Therefore, to a first approximation, these heavily deformed grains may be approximated by random parallel planes; as a consequence, the nucleation process may be assumed to take place on random parallel planes. The case of nucleation on random parallel planes and subsequent ellipsoidal growth is also possible. In this paper we model such situations employing time dependent germ grain processes with ellipsoidal growth. We provide explicit formulas for the mean volume and surface densities and related quantities. The known results for the spherical growth follow here as a particular case. Although this work has been done bearing applications to Materials Science in mind, the results obtained here may be applied to nucleation and growth reactions in general. Moreover, a generalization of the so called mean value property, crucial in finding explicit analytical formulas in the paper, is also provided as a further result in the Appendix A.Macroscopic fluxes and local reciprocal relation in second-order stochastic processes far from equilibrium.https://www.zbmath.org/1456.602012021-04-16T16:22:00+00:00"Ge, Hao"https://www.zbmath.org/authors/?q=ai:ge.haoAn inverse problem for the first-passage place of some diffusion processes with random starting point.https://www.zbmath.org/1456.601962021-04-16T16:22:00+00:00"Abundo, Mario"https://www.zbmath.org/authors/?q=ai:abundo.marioSummary: We study an inverse problem for the first-passage place of a one-dimensional diffusion process \(X(t)\) (also with jumps), starting from a random position \(\eta\in[a,b]\) Let be \(\tau_{a,b}\) the first time at which \(X(t)\) exits the interval \((a,b)\) and \(\pi_a=P(X(\tau_{a,b})\leq a)\) the probability of exit from the left of \((a,b)\) Given a probability \(q\in(0,1)\) the problem consists in finding the density \(g\) of \(\eta\) (if it exists) such that \(\pi_a=q\). Some explicit examples are reported.Consequences of nonconformist behaviors in a continuous opinion model.https://www.zbmath.org/1456.911032021-04-16T16:22:00+00:00"Vieira, Allan R."https://www.zbmath.org/authors/?q=ai:vieira.allan-r"Anteneodo, Celia"https://www.zbmath.org/authors/?q=ai:anteneodo.celia"Crokidakis, Nuno"https://www.zbmath.org/authors/?q=ai:crokidakis.nunoLinear stochastic thermodynamics for periodically driven systems.https://www.zbmath.org/1456.800122021-04-16T16:22:00+00:00"Proesmans, Karel"https://www.zbmath.org/authors/?q=ai:proesmans.karel"Cleuren, Bart"https://www.zbmath.org/authors/?q=ai:cleuren.bart"Van den Broeck, Christian"https://www.zbmath.org/authors/?q=ai:van-den-broeck.christianIrregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions.https://www.zbmath.org/1456.601662021-04-16T16:22:00+00:00"Marzougue, Mohamed"https://www.zbmath.org/authors/?q=ai:marzougue.mohamed"Sagna, Yaya"https://www.zbmath.org/authors/?q=ai:sagna.yayaSummary: In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.Review of median stable distributions and Schröder's equation.https://www.zbmath.org/1456.600502021-04-16T16:22:00+00:00"Bassett, Gib"https://www.zbmath.org/authors/?q=ai:bassett.gibSummary: Median stable distributions are an extension of traditional (mean) stable distributions. The traditional definition of stability (in terms of \textit{sums} of iid random variables) is recast as a condition on the sampling distribution of an estimator. For the traditional (mean) stable distribution, the sample mean's (rescaled) sampling distribution is identical to the distribution of the iid data. Median stable distributions are defined similarly by replacing the sample mean with the sample median. Since the sampling distribution of the median is a functional its stable distribution is the solution to a functional equation. It turns out that this defining functional equation is an instance of a famous equation due to \textit{E. Schroeder} [Math. Ann. 3, 296--322 (1871; JFM 02.0200.01)]. The fame of the equation is due to the way it incorporates iteration of functions, a key feature of what many years later would become dynamic systems analysis. The current paper reviews median stable distributions in light of its connection to Schröder's functional equation.The probability companion for engineering and computer science.https://www.zbmath.org/1456.600012021-04-16T16:22:00+00:00"Prügel-Bennett, Adam"https://www.zbmath.org/authors/?q=ai:prugel-bennett.adamFrom the cover of the book: ``This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in deep learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overview for students.''
The book is very large structured in the Preface, Nomenclature, 12 chapters (divided in 64 subchapters), Appendix A (divided in 12 subchapters), Appendix B (divided in 3 subchapters), Bibliography, Index:
Chapter 1. Introduction -- Chapter 2. Survey of distributions -- Chapter 3. Monte Carlo -- Chapter 4. Discrete random variables -- Chapter 5. The normal distribution -- Chapter 6. Handling experimental data -- Chapter 7. Mathematics of random variables -- Chapter 8. Bayes -- Chapter 9. Entropy -- Chapter 10. Collective behaviour -- Chapter 11. Markov chains -- Chapter 12. Stochastic processes -- Appendix A: Answers to exercises -- Appendix B: Probability distributions.
All the chapters contain examples and finish with exercises, thus we have more than 60 problems for solving. Most of the chapters contain hints for additional reading. The bibliography contains more than 70 references and the index more than 360 items. The short evaluations of the individual references in the bibliography are worth mentioning.
New in the book is the connection to machine learning methods, cp. Subchapter 8.5: Machine learning. The author wrote on page 254: ``There are an enormous number of books on Bayesian approaches to machine learning'', e.g., in the bibliography [\textit{D. Barber}, Bayesian reasoning and machine learning. Cambridge: Cambridge University Press (2012; Zbl 1267.68001); \textit{C. M. Bishop}, Pattern recognition and machine learning. New York, NY: Springer (2006; Zbl 1107.68072); \textit{C. E. Rasmussen} and \textit{C. K. I. Williams}, Gaussian processes for machine learning. Cambridge, MA: MIT Press (2006; Zbl 1177.68165); \textit{J. Pearl}, Probabilistic reasoning in intelligent systems: networks of plausible inference. San Mateo etc.: Morgan Kaufmann Publishers (1989; Zbl 0746.68089); \textit{D. J. C. MacKay}, Information theory, inference and learning algorithms. Cambridge: Cambridge University Press (2003; Zbl 1055.94001)].
The book can be very recommended all readers, who are interested in this field.
Reviewer: Ludwig Paditz (Dresden)Topology trivialization transition in random non-gradient autonomous ODEs on a sphere.https://www.zbmath.org/1456.829132021-04-16T16:22:00+00:00"Fyodorov, Y. V."https://www.zbmath.org/authors/?q=ai:fyodorov.yan-vFirst passage properties of a generalized Pólya urn.https://www.zbmath.org/1456.921212021-04-16T16:22:00+00:00"Kearney, Michael J."https://www.zbmath.org/authors/?q=ai:kearney.michael-j"Martin, Richard J."https://www.zbmath.org/authors/?q=ai:martin.richard-jCondition numbers for real eigenvalues in the real elliptic Gaussian ensemble.https://www.zbmath.org/1456.600192021-04-16T16:22:00+00:00"Fyodorov, Yan V."https://www.zbmath.org/authors/?q=ai:fyodorov.yan-v"Tarnowski, Wojciech"https://www.zbmath.org/authors/?q=ai:tarnowski.wojciechSummary: We study the distribution of the eigenvalue condition numbers \(\kappa_i = \sqrt{(\mathbf{l}_i^* \mathbf{l}_i) (\mathbf{r}_i^* \mathbf{r}_i)}\) associated with real eigenvalues \(\lambda_i\) of partially asymmetric \(N \times N\) random matrices from the real Elliptic Gaussian ensemble. The large values of \(\kappa_i\) signal the non-orthogonality of the (bi-orthogonal) set of left \(\mathbf{l}_i\) and right \(\mathbf{r}_i\) eigenvectors and enhanced sensitivity of the associated eigenvalues against perturbations of the matrix entries. We derive the general finite \(N\) expression for the joint density function (JDF) \(\mathcal{P}_N (z, t)\) of \(t = \kappa_i^2 - 1\) and \(\lambda_i\) taking value \(z\), and investigate its several scaling regimes in the limit \(N \rightarrow \infty\). When the degree of asymmetry is fixed as \(N \rightarrow \infty\), the number of real eigenvalues is \(\mathcal{O} (\sqrt{N})\), and in the bulk of the real spectrum \(t_i = \mathcal{O}(N)\), while on approaching the spectral edges the non-orthogonality is weaker: \(t_i = \mathcal{O} (\sqrt{N})\). In both cases the corresponding JDFs, after appropriate rescaling, coincide with those found in the earlier studied case of fully asymmetric (Ginibre) matrices. A different regime of weak asymmetry arises when a finite fraction of \(N\) eigenvalues remain real as \(N \rightarrow \infty\). In such a regime eigenvectors are weakly non-orthogonal, \(t = \mathcal{O}(1)\), and we derive the associated JDF, finding that the characteristic tail \(\mathcal{P} (z, t) \sim t^{-2}\) survives for arbitrary weak asymmetry. As such, it is the most robust feature of the condition number density for real eigenvalues of asymmetric matrices.Comparisons between largest and smallest order statistics from Pareto distributions.https://www.zbmath.org/1456.600552021-04-16T16:22:00+00:00"Ling, Jie"https://www.zbmath.org/authors/?q=ai:ling.jie"Fang, Longxiang"https://www.zbmath.org/authors/?q=ai:fang.longxiangSummary: In the paper, we discuss the problem of the stochastic comparisons of the largest and smallest order statistics from independent heterogeneous Pareto random variables with different scale and shape parameters. We study the reversed hazard rate order of smallest order statistics, usual stochastic order of the largest order statistics of type I in the sense of multivariate chain majorization. Furthermore, we investigat hazard rate order of smallest order statistics, usual stochastic order of the largest order statistics of type II in the sense of multivariate chain majorization and majorization orders respectively.Kernel estimations of the density distribution constructed by dependent observations and the accuracy of their approximation by \(L_1\) metric.https://www.zbmath.org/1456.620602021-04-16T16:22:00+00:00"Kvatadze, Zurab"https://www.zbmath.org/authors/?q=ai:kvatadze.zurab"Pharjiani, Beqnu"https://www.zbmath.org/authors/?q=ai:pharjiani.beqnuSummary: Kernel estimations of the Rosenblatt-Parzen type of unknown density distribution by conditionally independent and chain-dependent observations are constructed. The upper boundaries for the approximations of these densities constructed by estimates for \(L_1\) metric are determined. The obtained results are specified for the case of Bartlett kernel and smoothing coefficient \(a_n=\sqrt n\).Stochastic derivative of Poisson polynomial functionals and its application.https://www.zbmath.org/1456.601322021-04-16T16:22:00+00:00"Jaoshvili, Vakhtang"https://www.zbmath.org/authors/?q=ai:jaoshvili.vakhtang"Purtukhia, Omar"https://www.zbmath.org/authors/?q=ai:purtukhia.omar"Zerakidze, Zurab"https://www.zbmath.org/authors/?q=ai:zerakidze.zurabSummary: In the theory of stochastic integration, in contrast to the standard integration theory, besides the fact that the integrand is the measurable function of two variables, it should be the adapted (nonanticipated) process. \textit{A. V. Skorokhod} [Theory Probab. Appl. 20, 219--233 (1975; Zbl 0333.60060); translation from Teor. Veroyatn. Primen. 20, 223--238 (1975)] replaced this requirement with the requirement of smoothness in some sense of the integrand. \textit{B. Gaveau} and \textit{P. Trauber} [J. Funct. Anal. 46, 230--238 (1982; Zbl 0488.60068)] proved that the Skorokhod operator of stochastic integration coincides with the conjugate operator of a stochastic derivative (with the so-called Malliavin) operator. \textit{D. Ocone} [Stochastics 12, 161--185 (1984; Zbl 0542.60055)] proved that the integrand in the martingale representation theorem coincides with the predictable projection of the stochastic derivative of the functional. In the Weiner case there are two equivalent definitions of a stochastic derivative, but in general, for so called normal martingale classes these definitions are not equivalent. \textit{J. Ma} et al. [Bernoulli 4, No. 1, 81--114 (1998; Zbl 0897.60058)], built the corresponding example. In the present work, a new constructive definition of the stochastic derivative of the polynomial Poisson functional is introduced. It is shown that this definition is equivalent to a general definition based on a chaotic expansion of functional, and its properties are studied. The stochastic integral representation theorem with an explicit expression of the integrand is proved.On the concentration of large deviations for fat tailed distributions, with application to financial data.https://www.zbmath.org/1456.600652021-04-16T16:22:00+00:00"Filiasi, Mario"https://www.zbmath.org/authors/?q=ai:filiasi.mario"Livan, Giacomo"https://www.zbmath.org/authors/?q=ai:livan.giacomo"Marsili, Matteo"https://www.zbmath.org/authors/?q=ai:marsili.matteo"Peressi, Maria"https://www.zbmath.org/authors/?q=ai:peressi.maria"Vesselli, Erik"https://www.zbmath.org/authors/?q=ai:vesselli.erik"Zarinelli, Elia"https://www.zbmath.org/authors/?q=ai:zarinelli.eliaYoung-Stieltjes integrals with respect to Volterra covariance functions.https://www.zbmath.org/1456.601342021-04-16T16:22:00+00:00"Lim, Nengli"https://www.zbmath.org/authors/?q=ai:lim.nengliSummary: Complementary regularity between the integrand and integrator is a well known condition for the integral \(\int_0^Tf(r)\,\mathrm{d}g(r)\) to exist in the Riemann-Stieltjes sense. This condition also applies to the multi-dimensional case, in particular the 2D integral \(\int_{[0,T]^2}f(s,t)\,\mathrm{d}g(s,t)\). In the paper, we give a new condition for the existence of the integral under the assumption that the integrator \(g\) is a Volterra covariance function. We introduce the notion of strong Hölder bi-continuity, and show that if the integrand possess this property, the assumption on complementary regularity can be relaxed for the Riemann-Stieltjes sums of the integral to converge.Resonant activation in 2D and 3D systems driven by multi-variate Lévy noise.https://www.zbmath.org/1456.600922021-04-16T16:22:00+00:00"Szczepaniec, Krzysztof"https://www.zbmath.org/authors/?q=ai:szczepaniec.krzysztof"Dybiec, Bartłomiej"https://www.zbmath.org/authors/?q=ai:dybiec.bartlomiejRelative species abundance of replicator dynamics with sparse interactions.https://www.zbmath.org/1456.921512021-04-16T16:22:00+00:00"Obuchi, Tomoyuki"https://www.zbmath.org/authors/?q=ai:obuchi.tomoyuki"Kabashima, Yoshiyuki"https://www.zbmath.org/authors/?q=ai:kabashima.yoshiyuki"Tokita, Kei"https://www.zbmath.org/authors/?q=ai:tokita.keiAnalysis and stochastic processes on metric measure spaces.https://www.zbmath.org/1456.580192021-04-16T16:22:00+00:00"Grigor'yan, Alexander"https://www.zbmath.org/authors/?q=ai:grigoryan.alexanderThe purpose of the author is to survey some known results of the Laplacian operator on a geodesically complete and non-compact Riemannian manifold. Precisely, the overview contains, e.g., Semi-linear elliptic inequalities, Negative eigenvalues of Schrödinger, Estimates of the Green function, Heat kernels on connected sums, of Schrödinger operator, and of operators with singular drift, and so on. Likewise, the author deals with sections on Analysis on metric measure spaces and on Homology theory on graphs.
For the entire collection see [Zbl 1416.60012].
Reviewer: Mohammed El Aïdi (Bogotá)Duals of random vectors and processes with applications to prediction problems with missing values.https://www.zbmath.org/1456.622262021-04-16T16:22:00+00:00"Kasahara, Yukio"https://www.zbmath.org/authors/?q=ai:kasahara.yukio"Pourahmadi, Mohsen"https://www.zbmath.org/authors/?q=ai:pourahmadi.mohsen"Inoue, Akihiko"https://www.zbmath.org/authors/?q=ai:inoue.akihikoSummary: Important results in prediction theory dealing with missing values have been obtained traditionally using difficult techniques based on duality in Hilbert spaces of analytic functions [\textit{T. Nakazi}, Stud. Math. 78, 7--14 (1984; Zbl 0608.60040); \textit{A. G. Miamee} and \textit{M. Pourahmadi}, J. Lond. Math. Soc., II. Ser. 38, No. 1, 133--145 (1988; Zbl 0669.41018)]. We obtain and unify these results using a simple finite-dimensional duality lemma which is essentially an abstraction of a regression property of a multivariate normal random vector [\textit{M. M. Rao}, Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. B 8, 319--332 (1973; Zbl 0251.60034)] or its inverse covariance matrix. The approach reveals the roles of duality and biorthogonality of random vectors in dealing with infinite-dimensional and difficult prediction problems. A novelty of this approach is its reliance on the explicit representation of the prediction error in terms of the data rather than the predictor itself as in the traditional techniques. In particular, we find a new and explicit formula for the dual of the semi-finite process \(\{X_t;t\leq n\}\) for a fixed \(n\), which does not seem to be possible using the existing techniques.Singularities in large deviation functionals of bulk-driven transport models.https://www.zbmath.org/1456.826392021-04-16T16:22:00+00:00"Aminov, Avi"https://www.zbmath.org/authors/?q=ai:aminov.avi"Bunin, Guy"https://www.zbmath.org/authors/?q=ai:bunin.guy"Kafri, Yariv"https://www.zbmath.org/authors/?q=ai:kafri.yarivProduct matrix processes as limits of random plane partitions.https://www.zbmath.org/1456.600142021-04-16T16:22:00+00:00"Borodin, Alexei"https://www.zbmath.org/authors/?q=ai:borodin.alexei"Gorin, Vadim"https://www.zbmath.org/authors/?q=ai:gorin.vadim"Strahov, Eugene"https://www.zbmath.org/authors/?q=ai:strahov.eugeneSummary: We consider a random process with discrete time formed by squared singular values of products of truncations of Haar-distributed unitary matrices. We show that this process can be understood as a scaling limit of the Schur process, which gives determinantal formulas for (dynamical) correlation functions and a contour integral representation for the correlation kernel. The relation with the Schur processes implies that the continuous limit of marginals for q-distributed plane partitions coincides with the joint law of squared singular values for products of truncations of Haar-distributed random unitary matrices. We provide structural reasons for this coincidence that may also extend to other classes of random matrices.Probabilistic models of combinatorial schemes.https://www.zbmath.org/1456.600312021-04-16T16:22:00+00:00"Ènatskaya, Nataliya Yur'evna"https://www.zbmath.org/authors/?q=ai:enatskaya.n-yuSummary: An enumerative method is proposed for the analysis of combinatorial schemes in the pre-asymptotic region of variation of their parameters based on the construction of their probabilistic mathematical model, which represents for each scheme an iterative random process of sequential non-repeated formation of all its outcomes with a certain discipline of their numbering by unitary addition of certain elements of the scheme to a given value in it. Due to the importance for a number of studies of the scheme of recurrence of listing its outcomes, if it does not lie in its nature, it can be achieved by introducing into the scheme some restrictions that do not lead to a change in their set, do not change their probability and should be taken into account. The design of the process under the appropriate conditions of each scheme is graphically depicted by a graph with the probabilities of iterative transitions specified in it, which determine the final distribution on the set of its outcomes. On this basis, the problems of determining the number of outcomes of a scheme, establishing a one-to-one correspondence between numbers and types of its outcomes, called the numbering problem in direct and reverse statements, and finding the probability distribution of all its final outcomes are solved, which makes it possible to model them with the found distribution of playing out the outcome number and the subsequent determination of its modeled form by the result of solving the direct numbering problem. In the absence of an explicit formula for the number of outcomes of a scheme under certain conditions, an estimate of it can be obtained from the results of their modeling, followed by refinement of the numbering problem. The study of models of combinatorial schemes on random processes with the introduction of probabilistic parameters expands the possibilities of their use. The results of the analysis of schemes can be of a nature from numerical methods and algorithms to analytical in the form of recurrence relations and explicit formulas.Steady-state skewness and kurtosis from renormalized cumulants in (2 + 1)-dimensional stochastic surface growth.https://www.zbmath.org/1456.827212021-04-16T16:22:00+00:00"Singha, Tapas"https://www.zbmath.org/authors/?q=ai:singha.tapas"Nandy, Malay K."https://www.zbmath.org/authors/?q=ai:nandy.malay-kumarGaussian diffusion interrupted by Lévy walk.https://www.zbmath.org/1456.602202021-04-16T16:22:00+00:00"Weber, Piotr"https://www.zbmath.org/authors/?q=ai:weber.piotr"Pepłowski, Piotr"https://www.zbmath.org/authors/?q=ai:peplowski.piotrA randomly weighted minimum spanning tree with a random cost constraint.https://www.zbmath.org/1456.051462021-04-16T16:22:00+00:00"Frieze, Alan"https://www.zbmath.org/authors/?q=ai:frieze.alan-m"Tkocz, Tomasz"https://www.zbmath.org/authors/?q=ai:tkocz.tomaszSummary: We study the minimum spanning tree problem on the complete graph \(K_n\) where an edge \(e\) has a weight \(W_e\) and a cost \(C_e\), each of which is an independent copy of the random variable \(U^\gamma\) where \(\gamma\leq 1\) and \(U\) is the uniform \([0,1]\) random variable. There is also a constraint that the spanning tree \(T\) must satisfy \(C(T)\leq c_0\). We establish, for a range of values for \(c_0,\gamma \), the asymptotic value of the optimum weight via the consideration of a dual problem.Kramers' turnover phenomenon in the spatial diffusion region.https://www.zbmath.org/1456.602742021-04-16T16:22:00+00:00"Mondal, Shrabani"https://www.zbmath.org/authors/?q=ai:mondal.shrabani"Gupta, Bikash Chandra"https://www.zbmath.org/authors/?q=ai:chandra-gupta.bikash"Bag, Bidhan Chandra"https://www.zbmath.org/authors/?q=ai:bag.bidhan-chandraHigher order Cheeger inequalities for Steklov eigenvalues.https://www.zbmath.org/1456.580212021-04-16T16:22:00+00:00"Hassannezhad, Asma"https://www.zbmath.org/authors/?q=ai:hassannezhad.asma"Miclo, Laurent"https://www.zbmath.org/authors/?q=ai:miclo.laurentThe Steklov eigenvalue problem is the following boundary value problem
\[
\Delta u=0\text{ in }\Omega,\, \frac{\partial u}{\partial \nu}=\sigma u\text{ on }\partial\Omega,\tag{1}
\]
such that \(\Omega=(\Omega,g)\) is an \(n\)-dimensional compact Riemannian manifold endowed with a smooth boundary \(\partial \Omega\), \(\frac{\partial u}{\partial \nu}\) represents the directional derivative with respect to \(\nu\), the unit outward normal vector along \(\partial \Omega\), and \(\sigma\) is a real eigenvalue. The authors provide a lower bound of the \(k\)-th eigenvalue of \((1)\) in terms of the \(k\)-th Cheeger-Steklov constant. The authors also study the case when \((\Omega,g)\) is swapped by a probability measure space and by a finite state space, respectively.
Reviewer: Mohammed El Aïdi (Bogotá)The mechanism of additive composition.https://www.zbmath.org/1456.682182021-04-16T16:22:00+00:00"Tian, Ran"https://www.zbmath.org/authors/?q=ai:tian.ran"Okazaki, Naoaki"https://www.zbmath.org/authors/?q=ai:okazaki.naoaki"Inui, Kentaro"https://www.zbmath.org/authors/?q=ai:inui.kentaroSummary: Additive composition
[\textit{P. W. Foltz} et al., ``The measurement of textual coherence with latent semantic analysis'', Discourse Process 15, No. 2--3, 285--307 (1998; \url{doi:10.1080/01638539809545029});
\textit{T. K. Landauer} and \textit{S. T. Dumais}, ``A solution to Plato's problem: the latent semantic analysis theory of acquisition, induction, and representation of knowledge'', Psychol. Rev. 104, No. 2, 211--240 (1997; \url{doi:10.1037/0033-295X.104.2.211});
\textit{J. Mitchell} and \textit{M. Lapata}, ``Composition in distributional models of semantics'', Cognit. Sci. 34, No. 8, 1388--1429 (2010; \url{doi:10.1111/j.1551-6709.2010.01106.x})] is a widely used method for computing meanings of phrases, which takes the average of vector representations of the constituent words. In this article, we prove an upper bound for the bias of additive composition, which is the first theoretical analysis on compositional frameworks from a machine learning point of view. The bound is written in terms of collocation strength; we prove that the more exclusively two successive words tend to occur together, the more accurate one can guarantee their additive composition as an approximation to the natural phrase vector. Our proof relies on properties of natural language data that are empirically verified, and can be theoretically derived from an assumption that the data is generated from a Hierarchical Pitman-Yor Process. The theory endorses additive composition as a reasonable operation for calculating meanings of phrases, and suggests ways to improve additive compositionality, including: transforming entries of distributional word vectors by a function that meets a specific condition, constructing a novel type of vector representations to make additive composition sensitive to word order, and utilizing singular value decomposition to train word vectors.Geometric exponents, SLE and logarithmic minimal models.https://www.zbmath.org/1456.602162021-04-16T16:22:00+00:00"Saint-Aubin, Yvan"https://www.zbmath.org/authors/?q=ai:saint-aubin.yvan"Pearce, Paul A."https://www.zbmath.org/authors/?q=ai:pearce.paul-a"Rasmussen, Jørgen"https://www.zbmath.org/authors/?q=ai:rasmussen.jorgen-h|rasmussen.jorgen|rasmussen.jorgen-bornIntrinsic convergence properties of entropic sampling algorithms.https://www.zbmath.org/1456.600052021-04-16T16:22:00+00:00"Belardinelli, Rolando Elio"https://www.zbmath.org/authors/?q=ai:belardinelli.rolando-elio"Pereyra, Victor Daniel"https://www.zbmath.org/authors/?q=ai:pereyra.victor-daniel"Dickman, Ronald"https://www.zbmath.org/authors/?q=ai:dickman.ronald"Lourenço, Bruno Jeferson"https://www.zbmath.org/authors/?q=ai:lourenco.bruno-jefersonJensen's inequality under nonlinear expectation generated by BSDE with jumps.https://www.zbmath.org/1456.601562021-04-16T16:22:00+00:00"Zhang, Na"https://www.zbmath.org/authors/?q=ai:zhang.na"Jia, Guang-Yan"https://www.zbmath.org/authors/?q=ai:jia.guangyanSummary: In this paper, we study Jensen's inequality under \(f\)-expectation, which is a nonlinear expectation generated by backward stochastic differential equations (BSDEs) with jumps. We connect \(f\)-convex functions with the viscosity solutions of a kind of integral partial differential equations (IPDEs) with non-local terms. And find that under Lipschitz condition, the \(f\)-convex function is still convex in the usual sense, i.e., the jumps shrink the range of `convex' functions.Time-uniform Chernoff bounds via nonnegative supermartingales.https://www.zbmath.org/1456.600542021-04-16T16:22:00+00:00"Howard, Steven R."https://www.zbmath.org/authors/?q=ai:howard.steven-r"Ramdas, Aaditya"https://www.zbmath.org/authors/?q=ai:ramdas.aaditya-k"McAuliffe, Jon"https://www.zbmath.org/authors/?q=ai:mcauliffe.jon-d"Sekhon, Jasjeet"https://www.zbmath.org/authors/?q=ai:sekhon.jasjeet-sSummary: We develop a class of exponential bounds for the probability that a martingale sequence crosses a time-dependent linear threshold. Our key insight is that it is both natural and fruitful to formulate exponential concentration inequalities in this way. We illustrate this point by presenting a single assumption and theorem that together unify and strengthen many tail bounds for martingales, including classical inequalities (1960--80) by Bernstein, Bennett, Hoeffding, and Freedman; contemporary inequalities (1980--2000) by Shorack and Wellner, Pinelis, Blackwell, van de Geer, and de la Peña; and several modern inequalities (post-2000) by Khan, Tropp, Bercu and Touati, Delyon, and others. In each of these cases, we give the strongest and most general statements to date, quantifying the time-uniform concentration of scalar, matrix, and Banach-space-valued martingales, under a variety of nonparametric assumptions in discrete and continuous time. In doing so, we bridge the gap between existing line-crossing inequalities, the sequential probability ratio test, the Cramér-Chernoff method, self-normalized processes, and other parts of the literature.\(L^p\) solutions of BSDEs with a new kind of non-Lipschitz coefficients.https://www.zbmath.org/1456.601452021-04-16T16:22:00+00:00"Fan, Shengjun"https://www.zbmath.org/authors/?q=ai:fan.shengjun"Jiang, Long"https://www.zbmath.org/authors/?q=ai:jiang.longSummary: In this paper, we are interested in solving multidimensional backward stochastic differential equations (BSDEs) with a new kind of non-Lipschitz coefficients. We establish an existence and uniqueness result of the \(L^p (p > 1)\) solutions, which includes some known results as its particular cases.Asymmetric Lévy flights in nonhomogeneous environments.https://www.zbmath.org/1456.827952021-04-16T16:22:00+00:00"Srokowski, Tomasz"https://www.zbmath.org/authors/?q=ai:srokowski.tomaszWeighted distances in scale-free preferential attachment models.https://www.zbmath.org/1456.602572021-04-16T16:22:00+00:00"Jorritsma, Joost"https://www.zbmath.org/authors/?q=ai:jorritsma.joost"Komjáthy, Júlia"https://www.zbmath.org/authors/?q=ai:komjathy.juliaSummary: We study three preferential attachment models where the parameters are such that the asymptotic degree distribution has infinite variance. Every edge is equipped with a nonnegative i.i.d. weight. We study the weighted distance between two vertices chosen uniformly at random, the typical weighted distance, and the number of edges on this path, the typical hopcount. We prove that there are precisely two universality classes of weight distributions, called the explosive and conservative class. In the explosive class, we show that the typical weighted distance converges in distribution to the sum of two i.i.d. \textit{finite} random variables. In the conservative class, we prove that the typical weighted distance tends to infinity, and we give an explicit expression for the main growth term, as well as for the hopcount. Under a mild assumption on the weight distribution the fluctuations around the main term are tight.Modeling interacting dynamic networks. II: Systematic study of the statistical properties of cross-links between two networks with preferred degrees.https://www.zbmath.org/1456.824172021-04-16T16:22:00+00:00"Liu, Wenjia"https://www.zbmath.org/authors/?q=ai:liu.wenjia"Schmittmann, B."https://www.zbmath.org/authors/?q=ai:schmittmann.beate"Zia, R. K. P."https://www.zbmath.org/authors/?q=ai:zia.r-k-pRapid mixing of the switch Markov chain for strongly stable degree sequences.https://www.zbmath.org/1456.601752021-04-16T16:22:00+00:00"Amanatidis, Georgios"https://www.zbmath.org/authors/?q=ai:amanatidis.georgios"Kleer, Pieter"https://www.zbmath.org/authors/?q=ai:kleer.pieterSummary: The switch Markov chain has been extensively studied as the most natural Markov chain Monte Carlo approach for sampling graphs with prescribed degree sequences. We show that the switch chain for sampling simple undirected graphs with a given degree sequence is rapidly mixing when the degree sequence is so-called strongly stable. Strong stability is satisfied by all degree sequences for which the switch chain was known to be rapidly mixing based on Sinclair's multicommodity flow method up until a recent manuscript of \textit{P. Erdős} et al. in [``The mixing time of the switch Markov chains: a unified approach'', Preprint, \url{arXiv:1903.06600}]. Our approach relies on an embedding argument, involving a Markov chain defined by \textit{M. Jerrum} and \textit{A. Sinclair} in [Theor. Comput. Sci. 73, No. 1, 91--100 (1990; Zbl 0694.68044)]. This results in a much shorter proof that unifies (almost) all the rapid mixing results for the switch chain in the literature, and extends them up to sharp characterizations of P-stable degree sequences. In particular, our work resolves an open problem posed by \textit{C. Greenhill} and \textit{M. Sfragara} in [Theor. Comput. Sci. 719, 1--20 (2018; Zbl 1395.60079)].On extremals of the entropy production by ``Langevin-Kramers'' dynamics.https://www.zbmath.org/1456.827802021-04-16T16:22:00+00:00"Muratore-Ginanneschi, Paolo"https://www.zbmath.org/authors/?q=ai:muratore-ginanneschi.paoloInvertibility via distance for noncentered random matrices with continuous distributions.https://www.zbmath.org/1456.600282021-04-16T16:22:00+00:00"Tikhomirov, Konstantin"https://www.zbmath.org/authors/?q=ai:tikhomirov.konstantin-eSummary: Let \(A\) be an \(n \times n\) random matrix with independent rows \(R_1(A),\dots,R_n(A)\), and assume that for any \(i \leq n\) and any three-dimensional linear subspace \(F \subset \mathbb R^n\) the orthogonal projection of \(R_i(A)\) onto \(F\) has distribution density \(\rho(x): F\to \mathbb R_+\) satisfying \(\rho (x) \leq C_1 /\max (1, \| x\|_2^{2000}) (x \in F)\) for some constant \(C_1>0\). We show that for any fixed \(n \times n\) real matrix \(M\) we have
\[
\mathbb P \{s_{\min} (A+M) \leq tn^{-1/2}\} \leq C' \; t, \;\;\; t>0,
\]
where \(C' >0\) is a universal constant. In particular, the above result holds if the rows of \(A\) are independent centered log-concave random vectors with identity covariance matrices. Our method is free from any use of covering arguments, and is principally different from a standard approach involving a decomposition of the unit sphere and coverings, as well as an approach of Sankar-Spielman-Teng for noncentered Gaussian matrices [\textit{A. Sankar} et al., SIAM J. Matrix Anal. Appl. 28, No. 2, 446--476 (2006; Zbl 1179.65033)].Hyperuniform and rigid stable matchings.https://www.zbmath.org/1456.601212021-04-16T16:22:00+00:00"Klatt, Michael Andreas"https://www.zbmath.org/authors/?q=ai:klatt.michael-andreas"Last, Günter"https://www.zbmath.org/authors/?q=ai:last.gunter"Yogeshwaran, D."https://www.zbmath.org/authors/?q=ai:yogeshwaran.dhandapaniSummary: We study a stable partial matching \(\tau\) of the \(d\)-dimensional lattice with a stationary determinantal point process \(\Psi\) on \(\mathbb R^d\) with intensity \(\alpha >1\). For instance, \( \Psi\) might be a Poisson process. The matched points from \(\Psi\) form a stationary and ergodic (under lattice shifts) point process \(\Psi^\tau\) with intensity 1 that very much resembles \(\Psi\) for \(\alpha\) close to 1. On the other hand \(\Psi^\tau\) is hyperuniform and number rigid, quite in contrast to a Poisson process. We deduce these properties by proving more general results for a stationary point process \(\Psi \), whose so-called matching flower (a stopping set determining the matching partner of a lattice point) has a certain subexponential tail behavior. For hyperuniformity, we also additionally need to assume some mixing condition on \(\Psi \). Furthermore, if \(\Psi\) is a Poisson process then \(\Psi^\tau\) has an exponentially decreasing truncated pair correlation function.Two-step Markov update algorithm for accuracy-based learning classifier systems.https://www.zbmath.org/1456.681632021-04-16T16:22:00+00:00"Razeghi-Jahromi, Mohammad"https://www.zbmath.org/authors/?q=ai:razeghi-jahromi.mohammad"Nazmi, Shabnam"https://www.zbmath.org/authors/?q=ai:nazmi.shabnam"Homaifar, Abdollah"https://www.zbmath.org/authors/?q=ai:homaifar.abdollahSummary: In this paper, we investigate the impact of a two-step Markov update scheme for the reinforcement component of XCS, a family of accuracy-based learning classifier systems. We use a mathematical framework using discrete-time dynamical system theory to analyze the stability and convergence of the proposed method. We provide frequency domain analysis for classifier parameters to investigate the achieved improvement of the XCS algorithm, employing a two-step update rule in the transient and steady-state stages of learning. An experimental analysis is performed to learn to solve a multiplexer benchmark problem to compare the results of the proposed update rules with the original XCS. The results show faster convergence, better steady-state training accuracy and less sensitivity to variations in learning rates.On a generalisation of uniform distribution and its properties.https://www.zbmath.org/1456.620232021-04-16T16:22:00+00:00"Jayakumar, K."https://www.zbmath.org/authors/?q=ai:jayakumar.k-r"Sankaran, Kothamangalth Krishnan"https://www.zbmath.org/authors/?q=ai:sankaran.kothamangalth-krishnanSummary: \textit{S. Nadarajah} et al. [J. Stat. Comput. Simulation 83, No. 8, 1389--1404 (2013; Zbl 1453.62369)] introduced a family life time models using truncated negative binomial distribution and derived some properties of the family of distributions. It is a generalization of Marshall-Olkin family of distributions. In this paper, we introduce Generalized Uniform Distribution (GUD) using the approach of Nadarajah et al. [loc. cit.]. The shape properties of density function and hazard function are discussed. The expression for moments, order statistics, entropies are obtained. Estimation procedure is also discussed. The GDU introduced here is a generalization of the Marshall-Olkin extended uniform distribution studied in [\textit{K. K. Jose} and \textit{E. Krishna}, ProbStat Forum 4, Article No. 08, 78--88 (2011; Zbl 1235.62014)].A simplified proof of a theorem of A. N. Kolmogorov on the strong law of large numbers.https://www.zbmath.org/1456.600672021-04-16T16:22:00+00:00"Bobrov, A. A."https://www.zbmath.org/authors/?q=ai:bobrov.a-aSummary: In this note, we give a shorter proof of the well-known Kolmogorov's theorem on the strong law of large numbers. The method of proof is based on the properties of conditional mathematical expectations and the proof itself differs from Kolmogorov's only in a more compact use of these properties.A data-driven McMillan degree lower bound.https://www.zbmath.org/1456.370982021-04-16T16:22:00+00:00"Hokanson, Jeffrey M."https://www.zbmath.org/authors/?q=ai:hokanson.jeffrey-mSuperdiffusion driven by exponentially decaying memory.https://www.zbmath.org/1456.828292021-04-16T16:22:00+00:00"Alves, G. A."https://www.zbmath.org/authors/?q=ai:alves.gilvan-a"de Araújo, J. M."https://www.zbmath.org/authors/?q=ai:de-araujo.jose-milton"Cressoni, J. C."https://www.zbmath.org/authors/?q=ai:cressoni.j-c"da Silva, L. R."https://www.zbmath.org/authors/?q=ai:da-silva.luciano-r"da Silva, M. A. A."https://www.zbmath.org/authors/?q=ai:da-silva.marco-antonio-alves"Viswanathan, G. M."https://www.zbmath.org/authors/?q=ai:viswanathan.gandhimohan-mAnomalous diffusion and enhancement of diffusion in a vibrational motor.https://www.zbmath.org/1456.826602021-04-16T16:22:00+00:00"Guo, Wei"https://www.zbmath.org/authors/?q=ai:guo.wei"Du, Lu-Chun"https://www.zbmath.org/authors/?q=ai:du.luchun"Mei, Dong-Cheng"https://www.zbmath.org/authors/?q=ai:mei.dongchengCrossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz.https://www.zbmath.org/1456.602592021-04-16T16:22:00+00:00"Le Doussal, Pierre"https://www.zbmath.org/authors/?q=ai:le-doussal.pierreMutual entropy production in bipartite systems.https://www.zbmath.org/1456.825532021-04-16T16:22:00+00:00"Diana, Giovanni"https://www.zbmath.org/authors/?q=ai:diana.giovanni"Esposito, Massimiliano"https://www.zbmath.org/authors/?q=ai:esposito.massimilianoHyperbolic harmonic functions and hyperbolic Brownian motion.https://www.zbmath.org/1456.601942021-04-16T16:22:00+00:00"Eriksson, Sirkka-Liisa"https://www.zbmath.org/authors/?q=ai:eriksson.sirkka-liisa"Kaarakka, Terhi"https://www.zbmath.org/authors/?q=ai:kaarakka.terhiSummary: We study harmonic functions with respect to the Riemannian metric
\[ds^2=\frac{dx_1^2+\cdots +dx_n^2}{x_n^{\frac{2\alpha}{n-2}}}\] in the upper half space \(\mathbb{R}_+^n=\{(x_1,\dots,x_n) \in \mathbb{R}^n :x_n>0\}\). They are called \(\alpha\)-hyperbolic harmonic. An important result is that a function \(f\) is \(\alpha\)-hyperbolic harmonic íf and only if the function \(g(x) =x_n^{-\frac{2-n+\alpha}{2}}f(x)\) is the eigenfunction of the hyperbolic Laplace operator \(\triangle_h=x_n^2\triangle -(n-2) x_n\frac{\partial}{\partial x_n}\) corresponding to the eigenvalue \(\frac{1}{4} ((\alpha+1)^2-(n-1)^2)=0\). This means that in case \(\alpha =n-2\), the \(n-2\)-hyperbolic harmonic functions are harmonic with respect to the hyperbolic metric of the Poincaré upper half-space. We are presenting some connections of \(\alpha\)-hyperbolic functions to the generalized hyperbolic Brownian motion. These results are similar as in case of harmonic functions with respect to usual Laplace and Brownian motion.Discovering transition phenomena from data of stochastic dynamical systems with Lévy noise.https://www.zbmath.org/1456.370862021-04-16T16:22:00+00:00"Lu, Yubin"https://www.zbmath.org/authors/?q=ai:lu.yubin"Duan, Jinqiao"https://www.zbmath.org/authors/?q=ai:duan.jinqiaoSummary: It is a challenging issue to analyze complex dynamics from observed and simulated data. An advantage of extracting dynamic behaviors from data is that this approach enables the investigation of nonlinear phenomena whose mathematical models are unavailable. The purpose of this present work is to extract information about transition phenomena (e.g., mean exit time and escape probability) from data of stochastic differential equations with non-Gaussian Lévy noise. As a tool in describing dynamical systems, the Koopman semigroup transforms a nonlinear system into a linear system, but at the cost of elevating a finite dimensional problem into an infinite dimensional one. In spite of this, using the relation between the stochastic Koopman semigroup and the infinitesimal generator of a stochastic differential equation, we learn the mean exit time and escape probability from data. Specifically, we first obtain a finite dimensional approximation of the infinitesimal generator by an extended dynamic mode decomposition algorithm. Then, we identify the drift coefficient, diffusion coefficient, and anomalous diffusion coefficient for the stochastic differential equation. Finally, we compute the mean exit time and escape probability by finite difference discretization of the associated nonlocal partial differential equations. This approach is applicable in extracting transition information from data of stochastic differential equations with either (Gaussian) Brownian motion or (non-Gaussian) Lévy motion. We present one- and two-dimensional examples to demonstrate the effectiveness of our approach.
{\copyright 2020 American Institute of Physics}Book review of: D. V. Lindley, Understanding uncertainty.https://www.zbmath.org/1456.000422021-04-16T16:22:00+00:00"Tong, So Moon"https://www.zbmath.org/authors/?q=ai:tong.so-moonReview of [Zbl 1135.60002].A sufficient and necessary condition of PS-ergodicity of periodic measures and generated ergodic upper expectations.https://www.zbmath.org/1456.600712021-04-16T16:22:00+00:00"Feng, Chunrong"https://www.zbmath.org/authors/?q=ai:feng.chunrong"Qu, Baoyou"https://www.zbmath.org/authors/?q=ai:qu.baoyou"Zhao, Huaizhong"https://www.zbmath.org/authors/?q=ai:zhao.huaizhongBounds on the probability of radically different opinions.https://www.zbmath.org/1456.600522021-04-16T16:22:00+00:00"Burdzy, Krzysztof"https://www.zbmath.org/authors/?q=ai:burdzy.krzysztof"Pitman, Jim"https://www.zbmath.org/authors/?q=ai:pitman.jim-williamSummary: We establish bounds on the probability that two different agents, who share an initial opinion expressed as a probability distribution on an abstract probability space, given two different sources of information, may come to radically different opinions regarding the conditional probability of the same event.Spectral densities of singular values of products of Gaussian and truncated unitary random matrices.https://www.zbmath.org/1456.600262021-04-16T16:22:00+00:00"Neuschel, Thorsten"https://www.zbmath.org/authors/?q=ai:neuschel.thorstenSingular values of large non-central random matrices.https://www.zbmath.org/1456.600162021-04-16T16:22:00+00:00"Bryc, Włodek"https://www.zbmath.org/authors/?q=ai:bryc.wlodzimierz"Silverstein, Jack W."https://www.zbmath.org/authors/?q=ai:silverstein.jack-wAuthors' abstract: We study largest singular values of large random matrices, each with mean of a fixed rank K. Our main result is a limit theorem as the number of rows and columns approach infinity, while their ratio approaches a positive constant. It provides a decomposition of the largest K singular values into the deterministic rate of growth, random centered fluctuations given as explicit linear combinations of the entries of the matrix, and a term negligible in probability. We use this representation to establish asymptotic normality of the largest singular values for random matrices with means that have block structure. We also deduce asymptotic normality for the largest eigenvalues of a random matrix arising in a model of population genetics.
Reviewer: Göran Högnäs (Åbo)Collision of eigenvalues for matrix-valued processes.https://www.zbmath.org/1456.600212021-04-16T16:22:00+00:00"Jaramillo, Arturo"https://www.zbmath.org/authors/?q=ai:jaramillo.arturo"Nualart, David"https://www.zbmath.org/authors/?q=ai:nualart.davidFluctuations of a nonlinear stochastic heat equation in dimensions three and higher.https://www.zbmath.org/1456.601382021-04-16T16:22:00+00:00"Gu, Yu"https://www.zbmath.org/authors/?q=ai:gu.yu.1"Li, Jiawei"https://www.zbmath.org/authors/?q=ai:li.jiaweiAsymptotics for the systematic and idiosyncratic volatility with large dimensional high-frequency data.https://www.zbmath.org/1456.621722021-04-16T16:22:00+00:00"Kong, Xin-Bing"https://www.zbmath.org/authors/?q=ai:kong.xinbing"Lin, Jin-Guan"https://www.zbmath.org/authors/?q=ai:lin.jinguan"Liu, Guang-Ying"https://www.zbmath.org/authors/?q=ai:liu.guangyingUniform approximation of 2 dimensional Navier-Stokes equation by stochastic interacting particle systems.https://www.zbmath.org/1456.601652021-04-16T16:22:00+00:00"Flandoli, Franco"https://www.zbmath.org/authors/?q=ai:flandoli.franco"Olivera, Christian"https://www.zbmath.org/authors/?q=ai:olivera.christian"Simon, Marielle"https://www.zbmath.org/authors/?q=ai:simon.marielleAn averaging principle for stochastic switched systems with Lévy noise.https://www.zbmath.org/1456.370522021-04-16T16:22:00+00:00"Ma, Shuo"https://www.zbmath.org/authors/?q=ai:ma.shuo"Kang, Yanmei"https://www.zbmath.org/authors/?q=ai:kang.yanmeiSummary: In this paper, we present an averaging method for stochastic switched systems with Lévy noise under non-Lipschitz condition. With the help of successive approximation method and Bihari's inequality, the existence and uniqueness of the solutions of original and averaged systems are proved. Then, under suitable assumptions, we show that the solution of stochastic switched system with Lévy noise strongly converges to the solution of the corresponding averaged equation.Overdamped 2D Brownian motion for self-propelled and nonholonomic particles.https://www.zbmath.org/1456.602192021-04-16T16:22:00+00:00"Martinelli, Agostino"https://www.zbmath.org/authors/?q=ai:martinelli.agostinoMixed order transition and condensation in an exactly soluble one dimensional spin model.https://www.zbmath.org/1456.823372021-04-16T16:22:00+00:00"Bar, Amir"https://www.zbmath.org/authors/?q=ai:bar.amir"Mukamel, David"https://www.zbmath.org/authors/?q=ai:mukamel.davidErratum to: ``Conditionals and conditional probabilities without triviality''.https://www.zbmath.org/1456.600092021-04-16T16:22:00+00:00"Pruss, Alexander R."https://www.zbmath.org/authors/?q=ai:pruss.alexander-rErratum to the author's paper [ibid. 60, No. 3, 551--558 (2019; Zbl 1455.60007)].A note on the cross-covariance operator and on congruence relations for Hilbert space valued stochastic processes.https://www.zbmath.org/1456.621112021-04-16T16:22:00+00:00"King, David"https://www.zbmath.org/authors/?q=ai:king.david-a|king.david-jSummary: Explicit formulas are derived for the congruence mappings that connect three Hilbert spaces associated with a second-order stochastic process. In particular, an insightful expression is obtained for the mapping that connects a process to its corresponding reproducing kernel Hilbert space. In addition, a useful infinite dimensional extension of a result from \textit{C. G. Khatri} [Gujarat Stat. Rev. 3, No. 2, 21--23 (1976; Zbl 0341.62015)] which pertains to cross-covariance operators is provided.On Baxter type theorems for generalized random Gaussian processes with independent values.https://www.zbmath.org/1456.600872021-04-16T16:22:00+00:00"Krasnitskiy, S. M."https://www.zbmath.org/authors/?q=ai:krasnitskii.sergei-m"Kurchenko, O. O."https://www.zbmath.org/authors/?q=ai:kurchenko.oleksandr-oSummary: We construct suitable families of basic functions and prove theorems of Baxter type for generalized Gaussian random processes with independent values. These theorems are used to divide families of such processes into classes. The singularity of probability measures corresponding to representatives of different classes is proved.Numerical simulation of an anomalous diffusion process based on the higher-order accurate scheme.https://www.zbmath.org/1456.600082021-04-16T16:22:00+00:00"Moroz, L. I."https://www.zbmath.org/authors/?q=ai:moroz.l-i"Maslovskaya, A. G."https://www.zbmath.org/authors/?q=ai:maslovskaya.anna-gSummary: The paper is devoted to the development and program implementation of a computational algorithm for modeling a process of anomalous diffusion. The mathematical model is formulated as an initial-boundary value problem for a nonlinear fractional order partial differential equation. An implicit finite-difference scheme based on an increased accuracy order approximation for the Caputo derivative is constructed. An application program was designed to perform computer simulation of the anomalous diffusion process. The numerical analysis of the accuracy of approximate solutions is conducted using a test-problem. The results of computational experiments are presented on the example of the modeling of a fractal nonlinear dynamic reaction-diffusion system.An explicit second-order numerical scheme for mean-field forward backward stochastic differential equations.https://www.zbmath.org/1456.650082021-04-16T16:22:00+00:00"Sun, Yabing"https://www.zbmath.org/authors/?q=ai:sun.yabing"Zhao, Weidong"https://www.zbmath.org/authors/?q=ai:zhao.weidongSummary: In this paper, we propose an explicit second-order scheme for solving decoupled mean-field forward backward stochastic differential equations. Its stability is theoretically proved, and its error estimates are rigorously deduced, which show that the proposed scheme is of second-order accurate when the weak-order 2.0 Itô-Taylor scheme is used to solve mean-field stochastic differential equations. Some numerical experiments are presented to verify the theoretical results.TASEP fluctuations with soft-shock initial data.https://www.zbmath.org/1456.602652021-04-16T16:22:00+00:00"Quastel, Jeremy"https://www.zbmath.org/authors/?q=ai:quastel.jeremy"Rahman, Mustazee"https://www.zbmath.org/authors/?q=ai:rahman.mustazeeSummary: We consider the totally asymmetric simple exclusion process with \textit{soft-shock} initial particle density, which is a step function increasing in the direction of flow and the step size chosen small to admit KPZ scaling. The initial configuration is deterministic and the dynamics create a shock.
We prove that the fluctuations of a particle at the macroscopic position of the shock converge to the maximum of two independent GOE Tracy-Widom random variables, which establishes a conjecture of \textit{P. L. Ferrari} and \textit{P. Nejjar} [Probab. Theory Relat. Fields 161, No. 1--2, 61--109 (2015; Zbl 1311.60116)]. Furthermore, we show the joint fluctuations of particles near the shock are determined by the maximum of two lines described in terms of these two random variables. The microscopic position of the shock is then seen to be their difference.
Our proofs rely on determinantal formulae and a novel factorization of the associated kernels.Financial portfolios based on Tsallis relative entropy as the risk measure.https://www.zbmath.org/1456.911152021-04-16T16:22:00+00:00"Devi, Sandhya"https://www.zbmath.org/authors/?q=ai:devi.sandhyaRandom walks with preferential relocations and fading memory: a study through random recursive trees.https://www.zbmath.org/1456.602622021-04-16T16:22:00+00:00"Mailler, Cécile"https://www.zbmath.org/authors/?q=ai:mailler.cecile"Uribe, Bravo Gerónimo"https://www.zbmath.org/authors/?q=ai:uribe.bravo-geronimoSharp weak-type \((p,p)\) estimates \((1<p<\infty)\) for positive dyadic shifts.https://www.zbmath.org/1456.420232021-04-16T16:22:00+00:00"Osękowski, Adam"https://www.zbmath.org/authors/?q=ai:osekowski.adamSummary: The paper contains the study of sharp weak-type estimates for positive dyadic shifts on \(\mathbb{R}^d\). The proof exploits Bellman function method: the inequalities are deduced from the existence of certain associated special functions, enjoying appropriate majorization and concavity conditions.Dynamics of fluctuations in the Gaussian model with conserved dynamics.https://www.zbmath.org/1456.600642021-04-16T16:22:00+00:00"Corberi, Federico"https://www.zbmath.org/authors/?q=ai:corberi.federico"Mazzarisi, Onofrio"https://www.zbmath.org/authors/?q=ai:mazzarisi.onofrio"Gambassi, Andrea"https://www.zbmath.org/authors/?q=ai:gambassi.andreaStrong convergence theorem for Walsh-Kaczmarz-Fejér means.https://www.zbmath.org/1456.420352021-04-16T16:22:00+00:00"Gogolashvili, Nata"https://www.zbmath.org/authors/?q=ai:gogolashvili.nata"Nagy, Károly"https://www.zbmath.org/authors/?q=ai:nagy.karoly"Tephnadze, George"https://www.zbmath.org/authors/?q=ai:tephnadze.georgeSummary: As main result we prove that Fejér means of Walsh-Kaczmarz-Fourier series are uniformly bounded operators from the Hardy martingale space \(H_p\) to the Hardy martingale space \(H_p\) for \(0<p\leq 1/2\).Delay and noise induced regime shift and enhanced stability in gene expression dynamics.https://www.zbmath.org/1456.920672021-04-16T16:22:00+00:00"Yang, Tao"https://www.zbmath.org/authors/?q=ai:yang.tao"Zhang, Chun"https://www.zbmath.org/authors/?q=ai:zhang.chun"Zeng, Chunhua"https://www.zbmath.org/authors/?q=ai:zeng.chunhua"Zhou, Guoqiong"https://www.zbmath.org/authors/?q=ai:zhou.guoqiong"Han, Qinglin"https://www.zbmath.org/authors/?q=ai:han.qinglin"Tian, Dong"https://www.zbmath.org/authors/?q=ai:tian.dong"Zhang, Huili"https://www.zbmath.org/authors/?q=ai:zhang.huiliDynamics of non-Markovian exclusion processes.https://www.zbmath.org/1456.828652021-04-16T16:22:00+00:00"Khoromskaia, Diana"https://www.zbmath.org/authors/?q=ai:khoromskaia.diana"Harris, Rosemary J."https://www.zbmath.org/authors/?q=ai:harris.rosemary-j"Grosskinsky, Stefan"https://www.zbmath.org/authors/?q=ai:grosskinsky.stefanNonlinear Brownian dynamics of interfacial fluctuations in a shear flow.https://www.zbmath.org/1456.760532021-04-16T16:22:00+00:00"Thiébaud, Marine"https://www.zbmath.org/authors/?q=ai:thiebaud.marine"Amarouchene, Yacine"https://www.zbmath.org/authors/?q=ai:amarouchene.yacine"Bickel, Thomas"https://www.zbmath.org/authors/?q=ai:bickel.thomasQuadratic harvesting dominated optimal strategy for a stochastic single-species model.https://www.zbmath.org/1456.921272021-04-16T16:22:00+00:00"Zhao, Dianli"https://www.zbmath.org/authors/?q=ai:zhao.dianli"Liu, Haidong"https://www.zbmath.org/authors/?q=ai:liu.haidong"Zhou, Yanli"https://www.zbmath.org/authors/?q=ai:zhou.yanli"Yuan, Sanling"https://www.zbmath.org/authors/?q=ai:yuan.sanlingSummary: A stochastic population model with the mixed harvesting strategy is formulated and studied in this paper. Sufficient and necessary conditions for survival of the species are derived firstly. Then, based on the ergodic stationary distribution, the optimal strategy is identified. Results show that the linear harvesting effort threatens to the survival of the species; the quadratic harvesting strategy occupies an absolute advantage in the harvesting and excludes the linear part out of the optimal harvesting strategy. It's interest to see all these occur only in the random environments. Computer simulations are carried out to support the obtained results.Random walks in directed modular networks.https://www.zbmath.org/1456.824332021-04-16T16:22:00+00:00"Comin, Cesar H."https://www.zbmath.org/authors/?q=ai:comin.cesar-henrique"Viana, Mateus P."https://www.zbmath.org/authors/?q=ai:viana.mateus-p"Antiqueira, Lucas"https://www.zbmath.org/authors/?q=ai:antiqueira.lucas"Costa, Luciano Da F."https://www.zbmath.org/authors/?q=ai:costa.luciano-da-fontoura|da-f-costa.lucianoExact solution of master equation with Gaussian and compound Poisson noises.https://www.zbmath.org/1456.827712021-04-16T16:22:00+00:00"Huang, Guan-Rong"https://www.zbmath.org/authors/?q=ai:huang.guan-rong"Saakian, David B."https://www.zbmath.org/authors/?q=ai:saakian.david-b"Rozanova, Olga"https://www.zbmath.org/authors/?q=ai:rozanova.olga-s"Yu, Jui-Ling"https://www.zbmath.org/authors/?q=ai:yu.jui-ling"Hu, Chin-Kun"https://www.zbmath.org/authors/?q=ai:hu.chinkunIntegrable approach to simple exclusion processes with boundaries. Review and progress.https://www.zbmath.org/1456.812672021-04-16T16:22:00+00:00"Crampe, N."https://www.zbmath.org/authors/?q=ai:crampe.nicolas"Ragoucy, E."https://www.zbmath.org/authors/?q=ai:ragoucy.eric"Vanicat, M."https://www.zbmath.org/authors/?q=ai:vanicat.matthieuStrong approximation of iterated Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Application to numerical solution of Ito SDEs and semilinear SPDEs.https://www.zbmath.org/1456.650012021-04-16T16:22:00+00:00"Kuznetsov, Dmitriy Feliksovich"https://www.zbmath.org/authors/?q=ai:kuznetsov.dmitriy-feliksovichPublisher's description: The book is devoted to the strong approximation of iterated stochastic integrals in the context of numerical integration of Ito stochastic differential equations and non-commutative semilinear stochastic partial differential equations with nonlinear multiplicative trace class noise. The presented monograph open a new direction in researching of iterated Ito and Stratonovich stochastic integrals with respect to components of the multidimensional Wiener process. For the first time we successfully use the generalized multiple Fourier series (multiple Fourier-Legendre series as well as multiple trigonometric Fourier series) converging in the sense of norm in Hilbert space for the expansion and mean-square approximation of iterated Ito stochastic integrals of arbitrary multiplicity \(k\) (Chapter 1). The convergence with probability 1 as well as the convergence in the sense of \(n\)-th moment for the mentioned expansion have been proved \((n=2, 3,\dots)\). Moreover, the expansion for iterated Ito stochastic integrals is adapted for iterated Stratonovich stochastic integrals of multiplicities 1 to 5 (Chapter 2) as well as for some other types of iterated stochastic integrals (Chapter 1). Two theorems on expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity \(k\) based on generalized iterated Fourier series with pointwise convergence are formulated and proved (Chapter 2). The integration order replacement technique for the class of iterated Ito stochastic integrals has been introduced (Chapter 3). We derived the exact and approximate expressions for the mean-square approximation error of iterated Ito stochastic integrals of arbitrary multiplicity \(k\) (Chapter 1). Furthermore, we provided a significant practical material (Chapter 5) devoted to the expansions and approximations of specific iterated Ito and Stratonovich stochastic integrals of multiplicities 1 to 6 from the unified Taylor-Ito and Taylor-Stratonovich expansions (Chapter 4) using the system of Legendre polynomials and the system of trigonometric functions. The methods formulated in this book have been compared with some existing methods (Chapter 6). The results of Chapter 1 were applied (Chapter 7) to the approximation of iterated stochastic integrals of arbitrary multiplicity \(k\) with respect to the infinite-dimensional \(Q\)-Wiener process.Proportionate growth in patterns formed in the rotor-router model.https://www.zbmath.org/1456.051422021-04-16T16:22:00+00:00"Dandekar, Rahul"https://www.zbmath.org/authors/?q=ai:dandekar.rahul"Dhar, Deepak"https://www.zbmath.org/authors/?q=ai:dhar.deepakUnions of random trees and applications.https://www.zbmath.org/1456.050322021-04-16T16:22:00+00:00"James, Austen"https://www.zbmath.org/authors/?q=ai:james.austen"Larson, Matt"https://www.zbmath.org/authors/?q=ai:larson.matt"Montealegre, Daniel"https://www.zbmath.org/authors/?q=ai:montealegre.daniel"Salmon, Andrew"https://www.zbmath.org/authors/?q=ai:salmon.andrewSummary: \textit{S. Janson} [Math. Proc. Camb. Philos. Soc. 100, 319--330 (1986; Zbl 0622.60018)] showed that the number of edges in the union of \(k\) random spanning trees in the complete graph \(K_n\) is a shifted Poisson distribution. Using results from the theory of electrical networks, we provide a new proof of this result, and we obtain an explicit rate of convergence. This rate of convergence allows us to show a new upper tail bound on the number of trees in \(G ( n , p )\), for \(p\) a constant not depending on \(n\). The number of edges in the union of \(k\) random trees is related to moments of the number of spanning trees in \(G ( n , p )\).
As an application, we prove the law of the iterated logarithm for the number of spanning trees in \(G ( n , p )\). More precisely, consider the infinite random graph \(G ( \mathbb{N} , p )\), with vertex set \(\mathbb{N}\) and where each edge appears independently with constant probability \(p\). By restricting to \(\{ 1 , 2 , \ldots , n \}\), we obtain a series of nested Erdős-Réyni random graphs \(G ( n , p )\). We show that a scaled version of the number of spanning trees satisfies the law of the iterated logarithm.A lower bound for point-to-point connection probabilities in critical percolation.https://www.zbmath.org/1456.602662021-04-16T16:22:00+00:00"van den Berg, J."https://www.zbmath.org/authors/?q=ai:van-den-berg.j-c|van-den-berg.joachim|van-den-berg.jeroen-p|van-den-berg.jan-bouwe|van-den-berg.john-e|van-den-berg.rob|van-den-berg.johan-leo|van-den-berg.j-a|van-den-berg.j-i|van-den-berg.jur-p|van-den-berg.j-c.1|van-den-berg.jan"Don, H."https://www.zbmath.org/authors/?q=ai:don.henk|don.honsonSummary: Consider critical site percolation on \(\mathbb{Z}^d\) with \(d \geq 2\). We prove a lower bound of order \(n^{- d^2}\) for point-to-point connection probabilities, where \(n\) is the distance between the points.
Most of the work in our proof concerns a `construction' which finally reduces the problem to a topological one. This is then solved by applying a topological fact, Lemma 2.12 below, which follows from Brouwer's fixed point theorem.
Our bound improves the lower bound with exponent \(2 d (d-1)\), used by
\textit{R. Cerf} in [Ann. Probab. 43, No. 5, 2458--2480 (2015; Zbl 1356.60163)] to obtain an \textit{upper} bound for the so-called two-arm probabilities. Apart from being of interest in itself, our result gives a small improvement of the bound on the two-arm exponent found by Cerf.Gradual diffusive capture: slow death by many mosquito bites.https://www.zbmath.org/1456.921252021-04-16T16:22:00+00:00"Redner, S."https://www.zbmath.org/authors/?q=ai:redner.sidney"Bénichou, O."https://www.zbmath.org/authors/?q=ai:benichou.olivierHydrodynamically enforced entropic current of Brownian particles with a transverse gravitational force.https://www.zbmath.org/1456.826752021-04-16T16:22:00+00:00"Li, Feng-Guo"https://www.zbmath.org/authors/?q=ai:li.feng-guo"Ai, Bao-Quan"https://www.zbmath.org/authors/?q=ai:ai.baoquanLarge deviations of the shifted index number in the Gaussian ensemble.https://www.zbmath.org/1456.829782021-04-16T16:22:00+00:00"Pérez Castillo, Isaac"https://www.zbmath.org/authors/?q=ai:perez-castillo.isaacA reaction-subdiffusion model of fluorescence recovery after photobleaching (FRAP).https://www.zbmath.org/1456.920682021-04-16T16:22:00+00:00"Yuste, S. B."https://www.zbmath.org/authors/?q=ai:yuste.santos-bravo"Abad, E."https://www.zbmath.org/authors/?q=ai:abad.enrique"Lindenberg, K."https://www.zbmath.org/authors/?q=ai:lindenberg.katjaHydrodynamic limit of a \((2+1)\)-dimensional crystal growth model in the anisotropic KPZ class.https://www.zbmath.org/1456.601882021-04-16T16:22:00+00:00"Lerouvillois, Vincent"https://www.zbmath.org/authors/?q=ai:lerouvillois.vincentSummary: We study a model, introduced initially by \textit{D. J. Gates} and \textit{M. Westcott} [J. Stat. Phys. 81, No. 3--4, 681--715 (1995; Zbl 1107.60325)] to describe crystal growth evolution, which belongs to the anisotropic KPZ universality class [\textit{M. Prähofer} and \textit{H. Spohn}, J. Stat. Phys. 88, No. 5--6, 999--1012 (1997; Zbl 0945.82543)]. It can be thought of as a \((2+1)\)-dimensional generalisation of the well known \((1+1)\)-dimensional polynuclear growth model (PNG). We show the full hydrodynamic limit of this process i.e the convergence of the random interface height profile after ballistic space-time scaling to the viscosity solution of a Hamilton-Jacobi PDE: \(\partial_{t}u = v(\nabla u)\) with \(v\) an explicit non-convex speed function. The convergence holds in the strong almost sure sense.Attracting random walks.https://www.zbmath.org/1456.601772021-04-16T16:22:00+00:00"Gaudio, Julia"https://www.zbmath.org/authors/?q=ai:gaudio.julia"Polyanskiy, Yury"https://www.zbmath.org/authors/?q=ai:polyanskiy.yurySummary: This paper introduces the attracting random walks model, which describes the dynamics of a system of particles on a graph with \(n\) vertices. At each step, a single particle moves to an adjacent vertex (or stays at the current one) with probability proportional to the exponent of the number of other particles at a vertex. From an applied standpoint, the model captures the \textit{rich get richer} phenomenon. We show that the Markov chain exhibits a phase transition in mixing time, as the parameter governing the attraction is varied. Namely, mixing time is \(O(n\log n)\) when the temperature is sufficiently high and \(\exp (\Omega (n))\) when temperature is sufficiently low. When \(\mathcal{G}\) is the complete graph, the model is a projection of the Potts model, whose mixing properties and the critical temperature have been known previously. However, for any other graph our model is non-reversible and does not seem to admit a simple Gibbsian description of a stationary distribution. Notably, we demonstrate existence of the dynamic phase transition without decomposing the stationary distribution into phases.The speed of the tagged particle in the exclusion process on Galton-Watson trees.https://www.zbmath.org/1456.602552021-04-16T16:22:00+00:00"Gantert, Nina"https://www.zbmath.org/authors/?q=ai:gantert.nina"Schmid, Dominik"https://www.zbmath.org/authors/?q=ai:schmid.dominikSummary: We study two different versions of the simple exclusion process on augmented Galton-Watson trees, the constant speed model and the variable speed model. In both cases, the simple exclusion process starts from an equilibrium distribution with non-vanishing particle density. Moreover, we assume to have initially a particle in the root, the tagged particle. We show for both models that the tagged particle has a positive linear speed and we give explicit formulas for the speeds.Komatu-Loewner differential equations.https://www.zbmath.org/1456.300212021-04-16T16:22:00+00:00"Fukushima, Masatoshi"https://www.zbmath.org/authors/?q=ai:fukushima.masatoshiThe author describes the Komatu-Loewner differential equation for the standard slit domain, annulus and circularly slit annulus. Given a Jordan arc \(\gamma=\{\gamma(t):0\leq t\leq t_{\gamma}\}\), \(\gamma(0)\in\mathbb R\), \(\gamma(0,t_{\gamma}]\subset\mathbb H=\{z\in\mathbb C:\text{Im}\,z>0\}\), there exists a unique Riemann map \(g_t\), \(0<t\leq t_{\gamma}\), from \(\mathbb H\setminus\gamma(0,t]\) onto \(\mathbb H\) satisfying \(\lim_{z\to\infty}(g_t(z)-z)=0\) and, under a suitable continuous reparametrization of \(t\), \(g_t\) obeys a Loewner differential equation \[\frac{dg_t(z)}{dt}=\frac{2}{g_t(z)-\xi(t)},\;\;\;z\in\mathbb H\setminus\gamma(0,t],\;\;\;g_0(z)=z,\] where \(\xi(t)\) is a continuous real-valued driving function. The Komatu-Loewner differential equation is an extension of the Loewner equation to annulus and circularly slit annulus. The author aims to explain in detail how to establish these Komatu-Loewner equations as genuine ordinary differential equations. The second aim of the paper is to give a brief account of a Komatu-Loewner evolution \(\{F_t\}\) of growing hulls driven by the pair \((\xi(t),{\mathbf s}(t))\), where \({\mathbf s}(t)\) is a motion of slits. Both expositions follow the lines of recent author's joint articles.
Reviewer: Dmitri V. Prokhorov (Saratov)A decorated tree approach to random permutations in substitution-closed classes.https://www.zbmath.org/1456.600302021-04-16T16:22:00+00:00"Borga, Jacopo"https://www.zbmath.org/authors/?q=ai:borga.jacopo"Bouvel, Mathilde"https://www.zbmath.org/authors/?q=ai:bouvel.mathilde"Féray, Valentin"https://www.zbmath.org/authors/?q=ai:feray.valentin"Stufler, Benedikt"https://www.zbmath.org/authors/?q=ai:stufler.benediktThis paper analyzes random permutations from substitution-closed classes via a probabilistic approach. Given a substitution-closed class \(C\) with the set \(S\) of simple permutations for \(i\) in \([n]\), the generating function of \(S\) is also denoted by \(S\) for convenience. Its radius of convergence is denoted by \(\rho_S\). For a permutation \(v\) and a pattern \(\pi\), denote by \(c\)-\(occ(\pi,v)\) the number of consecutive occurrences of pattern \(\pi\) in \(v\). Suppose that \(S'(\rho_S)\ge1/(1+\rho_S)^2-1\). Consider a uniform random permutation \(v_n\) of size \(n\) in \(C\), where \(n\) is any positive integer. By identifying the packed forest associated with a uniform random permutation in a substitution-closed class as a conditioned mono-type Galton-Waston forest, it is shown that for each pattern \(\pi\in C\), there exists \(\gamma\in[0,1]\) such that \(\frac1n c\)-\(occ(\pi,v_n)\rightarrow\gamma\) in probability as \(n\) tends to infinity.
Reviewer: Yilun Shang (Newcastle)KPZ equation tails for general initial data.https://www.zbmath.org/1456.602532021-04-16T16:22:00+00:00"Corwin, Ivan"https://www.zbmath.org/authors/?q=ai:corwin.ivan"Ghosal, Promit"https://www.zbmath.org/authors/?q=ai:ghosal.promitSummary: We consider the upper and lower tail probabilities for the centered (by time\(/24)\) and scaled (according to KPZ \(\text{time}^{1/3}\) scaling) one-point distribution of the Cole-Hopf solution of the KPZ equation when started with initial data drawn from a very general class. For the lower tail, we prove an upper bound which demonstrates a crossover from super-exponential decay with exponent \(3\) in the shallow tail to an exponent \(5/2\) in the deep tail. For the upper tail, we prove super-exponential decay bounds with exponent \(3/2\) at all depths in the tail.Density-matrix based numerical methods for discovering order and correlations in interacting systems.https://www.zbmath.org/1456.600072021-04-16T16:22:00+00:00"Henley, Christopher L."https://www.zbmath.org/authors/?q=ai:henley.christopher-l"Changlani, Hitesh J."https://www.zbmath.org/authors/?q=ai:changlani.hitesh-jOn the well-posedness of coupled forward-backward stochastic differential equations driven by Teugels martingales.https://www.zbmath.org/1456.601462021-04-16T16:22:00+00:00"Guerdouh, Dalila"https://www.zbmath.org/authors/?q=ai:guerdouh.dalila"Khelfallah, Nabil"https://www.zbmath.org/authors/?q=ai:khelfallah.nabil"Mezerdi, Brahim"https://www.zbmath.org/authors/?q=ai:mezerdi.brahimSummary: We deal with a class of fully coupled forward-backward stochastic differential equations (FBSDEs), driven by Teugels martingales associated with a general Lévy process. Under some assumptions on the derivatives of the coefficients, we prove the existence and uniqueness of a global solution on an arbitrarily large time interval. Moreover, we establish stability and comparison theorems for the solutions of such equations. Note that the present work extends known results proved for FBSDEs driven by a Brownian motion, by using martingale techniques related to jump processes, to overcome the lack of continuity.The identification problem for BSDEs driven by possibly non-quasi-left-continuous random measures.https://www.zbmath.org/1456.602242021-04-16T16:22:00+00:00"Bandini, Elena"https://www.zbmath.org/authors/?q=ai:bandini.elena"Russo, Francesco"https://www.zbmath.org/authors/?q=ai:russo.francesco.2On spectral eigenvalue problem of a class of self-similar spectral measures with consecutive digits.https://www.zbmath.org/1456.420332021-04-16T16:22:00+00:00"Wang, Cong"https://www.zbmath.org/authors/?q=ai:wang.cong"Wu, Zhi-Yi"https://www.zbmath.org/authors/?q=ai:wu.zhi-yiSummary: Let \(\mu_{p,q}\) be a self-similar spectral measure with consecutive digits generated by an iterated function system \(\{f_i(x)=\frac{x}{p}+\frac{i}{q}\}_{i=0}^{q-1} \), where \(2\le q\in\mathbb{Z}\) and \(q|p\). It is known that for each \(w=w_1w_2\cdots \in \{-1,1\}^\infty :=\{i_1i_2\cdots :\text{ all }i_k \in \{-1,1\}\} \), the set
\[
\Lambda_w=\left\{\sum_{j=1}^na_j w_j p^{j-1}:a_j\in \{0,1,\ldots ,q-1\},n\geq 1\right\}
\]
is a spectrum of \(\mu_{p,q}\). In this paper, we study the possible real number \(t\) such that the set \(t\Lambda_w\) are also spectra of \(\mu_{p,q}\) for all \(w\in \{-1,1\}^\infty\).Spatial dynamics in interacting systems with discontinuous coefficients and their continuum limits.https://www.zbmath.org/1456.601552021-04-16T16:22:00+00:00"Zanco, Giovanni"https://www.zbmath.org/authors/?q=ai:zanco.giovanniBig jobs arrive early: from critical queues to random graphs.https://www.zbmath.org/1456.602382021-04-16T16:22:00+00:00"Bet, Gianmarco"https://www.zbmath.org/authors/?q=ai:bet.gianmarco"van der Hofstad, Remco"https://www.zbmath.org/authors/?q=ai:van-der-hofstad.remco-w"van Leeuwaarden, Johan S. H."https://www.zbmath.org/authors/?q=ai:van-leeuwaarden.johan-s-hSummary: We consider a queue to which only a finite pool of \(n\) customers can arrive, at times depending on their service requirement. A customer with stochastic service requirement \(S\) arrives to the queue after an exponentially distributed time with mean \(S^{-\alpha}\) for some \(\alpha \in [0,1]\); therefore, larger service requirements trigger customers to join earlier. This finite-pool queue interpolates between two previously studied cases: \(\alpha = 0\) gives the so-called \(\Delta_{(i)}/G/1\) queue and \(\alpha = 1\) is closely related to the exploration process for inhomogeneous random graphs. We consider the asymptotic regime in which the pool size \(n\) grows to infinity and establish that the scaled queue-length process converges to a diffusion process with a negative quadratic drift. We leverage this asymptotic result to characterize the head start that is needed to create a long period of activity. We also describe how this first busy period of the queue gives rise to a critically connected random forest.Transform methods for heavy-traffic analysis.https://www.zbmath.org/1456.602402021-04-16T16:22:00+00:00"Hurtado-Lange, Daniela"https://www.zbmath.org/authors/?q=ai:hurtado-lange.daniela"Theja Maguluri, Siva"https://www.zbmath.org/authors/?q=ai:maguluri.siva-thejaSummary: The drift method was recently developed to study queuing systems in steady state. It was used successfully to obtain bounds on the moments of the scaled queue lengths that are asymptotically tight in heavy traffic and in a wide variety of systems, including generalized switches, input-queued switches, bandwidth-sharing networks, and so on. In this paper, we develop the use of transform techniques for heavy-traffic analysis, with a special focus on the use of moment-generating functions. This approach simplifies the proofs of the drift method and provides a new perspective on the drift method. We present a general framework and then use the moment-generating function method to obtain the stationary distribution of scaled queue lengths in heavy traffic in queuing systems that satisfy the complete resource pooling condition. In particular, we study load balancing systems and generalized switches under general settings.Weak well-posedness of multidimensional stable driven SDEs in the critical case.https://www.zbmath.org/1456.601432021-04-16T16:22:00+00:00"Chaudru de Raynal, Paul-Éric"https://www.zbmath.org/authors/?q=ai:de-raynal.paul-eric-chaudru"Menozzi, Stéphane"https://www.zbmath.org/authors/?q=ai:menozzi.stephane"Priola, Enrico"https://www.zbmath.org/authors/?q=ai:priola.enricoRotational invariance of stochastic processes with application to fractional dynamics.https://www.zbmath.org/1456.600742021-04-16T16:22:00+00:00"Ślezak, Jakub K."https://www.zbmath.org/authors/?q=ai:slezak.jakub-karol"Magdziarz, Marcin"https://www.zbmath.org/authors/?q=ai:magdziarz.marcinOn dual Bernstein polynomials and stochastic fractional integro-differential equations.https://www.zbmath.org/1456.601672021-04-16T16:22:00+00:00"Sayevand, Khosro"https://www.zbmath.org/authors/?q=ai:sayevand.khosro"Machado, J. Tenreiro"https://www.zbmath.org/authors/?q=ai:machado.jose-antonio-tenreiro"Masti, Iman"https://www.zbmath.org/authors/?q=ai:masti.imanSummary: In recent years, random functional or stochastic equations have been reported in a large class of problems. In many cases, an exact analytical solution of such equations is not available and, therefore, is of great importance to obtain their numerical approximation. This study presents a numerical technique based on Bernstein operational matrices for a family of stochastic fractional integro-differential equations (SFIDE) by means of the trapezoidal rule. A relevant feature of this method is the conversion of the SFIDE into a linear system of algebraic equations that can be analyzed by numerical methods. An upper error bound, the convergence, and error analysis of the scheme are investigated. Three examples illustrate the accuracy and performance of the technique.Beyond Itô versus Stratonovich.https://www.zbmath.org/1456.601682021-04-16T16:22:00+00:00"Yuan, Ruoshi"https://www.zbmath.org/authors/?q=ai:yuan.ruoshi"Ao, Ping"https://www.zbmath.org/authors/?q=ai:ao.pingOn hyperbolic decay of prediction error variance for deterministic stationary sequences.https://www.zbmath.org/1456.600772021-04-16T16:22:00+00:00"Babayan, N. M."https://www.zbmath.org/authors/?q=ai:babayan.n-m.1"Ginovyan, M. S."https://www.zbmath.org/authors/?q=ai:ginovyan.mamikon-sSummary: One of the main problems in prediction theory of second-order stationary processes, called direct prediction problem, is to describe the asymptotic behavior of the best linear mean squared one-step ahead prediction error variance in predicting the value \(X(0)\) of a stationary process \(X(t)\) by the observed past of finite length \(n\) as \(n\) goes to infinity, depending on the regularity nature (deterministic or non-deterministic) of the underlying observed process \(X(t)\). In this paper, we obtain sufficient conditions for hyperbolic decay of prediction error variance for deterministic stationary sequences, generalizing a result obtained by
\textit{M. Rosenblatt} [J. Math. Mech. 6, 801--810 (1957; Zbl 0080.35001)].On single-layer potentials for a class of pseudo-differential equations related to linear transformations of a symmetric \(\alpha \)-stable stochastic process.https://www.zbmath.org/1456.601202021-04-16T16:22:00+00:00"Mamalyha, Kh. V."https://www.zbmath.org/authors/?q=ai:mamalyha.kh-v"Osypchuk, M. M."https://www.zbmath.org/authors/?q=ai:osypchuk.m-mSummary: In this article an arbitrary invertible linear transformations of a symmetric \(\alpha \)-stable stochastic process in \(d\)-dimensional Euclidean space \(\mathbb{R}^d\) are investigated. The result of such transformation is a Markov process in \(\mathbb{R}^d\) whose generator is the pseudo-differential operator defined by its symbol \((-(Q\xi,\xi)^{\alpha/2})_{\xi\in\mathbb{R}^d}\) with some symmetric positive definite \(d\times d\)-matrix \(Q\) and fixed exponent \(\alpha\in(1,2)\). The transition probability density of this process is the fundamental solution of some parabolic pseudo-differential equation. The notion of a single-layer potential for that equation is introduced and its properties are investigated. In particular, an operator is constructed whose role in our consideration is analogous to that the gradient in the classical theory. An analogy to the classical theorem on the jump of the co-normal derivative of the single-layer potential is proved. This result can be applied for solving some boundary-value problems for the parabolic pseudo-differential equations under consideration. For \(\alpha = 2 \), the process under consideration is a linear transformation of Brownian motion, and all the investigated properties of the single-layer potential are well known.Overruled harmonic explorers in the plane and stochastic Löwner evolution.https://www.zbmath.org/1456.602122021-04-16T16:22:00+00:00"Celani, A."https://www.zbmath.org/authors/?q=ai:celani.antonio"Mazzino, A."https://www.zbmath.org/authors/?q=ai:mazzino.andrea"Tizzi, M."https://www.zbmath.org/authors/?q=ai:tizzi.marcoMulticritical continuous random trees.https://www.zbmath.org/1456.824312021-04-16T16:22:00+00:00"Bouttier, J."https://www.zbmath.org/authors/?q=ai:bouttier.jeremie"Di Francesco, P."https://www.zbmath.org/authors/?q=ai:di-francesco.philippe"Guitter, E."https://www.zbmath.org/authors/?q=ai:guitter.emmanuelApparent superluminal velocities and random walk in the velocity space.https://www.zbmath.org/1456.830052021-04-16T16:22:00+00:00"Sen, Abhijit"https://www.zbmath.org/authors/?q=ai:sen.abhijit"Silagadze, Zurab K."https://www.zbmath.org/authors/?q=ai:silagadze.zurab-kTheoretical investigation of totally asymmetric exclusion processes on lattices with junctions.https://www.zbmath.org/1456.826902021-04-16T16:22:00+00:00"Pronina, Ekaterina"https://www.zbmath.org/authors/?q=ai:pronina.ekaterina"Kolomeisky, Anatoly B."https://www.zbmath.org/authors/?q=ai:kolomeisky.anatoly-bStatistics of branched populations split into different types.https://www.zbmath.org/1456.921182021-04-16T16:22:00+00:00"Huillet, Thierry E."https://www.zbmath.org/authors/?q=ai:huillet.thierry-eSummary: Some population is made of \(n\) individuals that can be of \(P\) possible species (or types) at equilibrium. How are individuals scattered among types? We study two random scenarios of such species abundance distributions. In the first one, each species grows from independent founders according to a Galton-Watson branching process. When the number of founders \(P\) is either fixed or random (either Poisson or geometrically-distributed), a question raised is: given a population of \(n\) individuals as a whole, how does it split into the species types? This model is one pertaining to forests of Galton-Watson trees. A second scenario that we will address in a similar way deals with forests of increasing trees. Underlying this setup, the creation/annihilation of clusters (trees) is shown to result from a recursive nucleation/aggregation process as one additional individual is added to the total population.On a multiserver queueing system with customers' impatience until the end of service under single and multiple-vacation policies.https://www.zbmath.org/1456.602432021-04-16T16:22:00+00:00"Kadi, Mokhtar"https://www.zbmath.org/authors/?q=ai:kadi.mokhtar"Bouchentouf, Amina Angelika"https://www.zbmath.org/authors/?q=ai:bouchentouf.amina-angelika"Yahiaoui, Lahcene"https://www.zbmath.org/authors/?q=ai:yahiaoui.lahceneSummary: This paper deals with a multiserver queueing system with Bernoulli feedback and impatient customers (balking and reneging) under synchronous multiple and single vacation policies. Reneged customers may be retained in the system. Using probability generating functions (PGFs) technique, we formally obtain the steady-state solution of the proposed queueing system. Further, important performance measures and cost model are derived. Finally, numerical examples are presented.Local large deviation principle for Wiener process with random resetting.https://www.zbmath.org/1456.600662021-04-16T16:22:00+00:00"Logachov, A."https://www.zbmath.org/authors/?q=ai:logachov.artem-vasilevich|logachov.artem-v"Logachova, O."https://www.zbmath.org/authors/?q=ai:logachova.olga-m"Yambartsev, A."https://www.zbmath.org/authors/?q=ai:yambartsev.anatoly-a|yambartsev.anatoliStrong Kac's chaos in the mean-field Bose-Einstein condensation.https://www.zbmath.org/1456.601972021-04-16T16:22:00+00:00"Albeverio, Sergio"https://www.zbmath.org/authors/?q=ai:albeverio.sergio-a"De Vecchi, Francesco C."https://www.zbmath.org/authors/?q=ai:de-vecchi.francesco-c"Romano, Andrea"https://www.zbmath.org/authors/?q=ai:romano.andrea"Ugolini, Stefania"https://www.zbmath.org/authors/?q=ai:ugolini.stefaniaA note on large deviations for unbounded observables.https://www.zbmath.org/1456.370092021-04-16T16:22:00+00:00"Nicol, Matthew"https://www.zbmath.org/authors/?q=ai:nicol.matthew"Török, Andrew"https://www.zbmath.org/authors/?q=ai:torok.andreiThe authors prove exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. The main results of the paper is the following: uniform expansion does not imply existence of a rate function for unbounded observables, no matter the tail behavior of the cumulative distribution function. Typical examples include: exponential decay of autocorrelations, exponential decay under the transfer operators, and strictly stretched exponential large deviations.
Reviewer: George Stoica (Saint John)Forward controllability of a random attractor for the non-autonomous stochastic sine-Gordon equation on an unbounded domain.https://www.zbmath.org/1456.350432021-04-16T16:22:00+00:00"Yang, Shuang"https://www.zbmath.org/authors/?q=ai:yang.shuang"Li, Yangrong"https://www.zbmath.org/authors/?q=ai:li.yangrongSummary: A pullback random attractor is called forward controllable if its time-component is semi-continuous to a compact set in the future, and the minimum among all such compact limit-sets is called a forward controller. The existence of a forward controller closely relates to the forward compactness of the attractor, which is further argued by the forward-pullback asymptotic compactness of the system. The abstract results are applied to the non-autonomous stochastic sine-Gordon equation on an unbounded domain. The existence of a forward compact attractor is proved, which leads to the existence of a forward controller. The measurability of the attractor is proved by considering two different universes.Exit time asymptotics for dynamical systems with fast random switching near an unstable equilibrium.https://www.zbmath.org/1456.601392021-04-16T16:22:00+00:00"Bakhtin, Yuri"https://www.zbmath.org/authors/?q=ai:bakhtin.yuri-yu"Gaál, Alexisz"https://www.zbmath.org/authors/?q=ai:gaal.alexisz-tamasDerivation formulas of noncausal finite variation processes from the stochastic Fourier coefficients.https://www.zbmath.org/1456.601312021-04-16T16:22:00+00:00"Hoshino, Kiyoiki"https://www.zbmath.org/authors/?q=ai:hoshino.kiyoikiSummary: Let \((B_t)_{t\in [0,\infty)}\) be a real Brownian motion on a probability space \((\Omega ,\mathcal{F},P)\). Our concern is whether and how a noncausal type stochastic differential \(dX_t=a(t,\omega)\,dB_t+b(t,\omega)\,dt\) is determined from its stochastic Fourier coefficients (SFCs for short) \((e_n,dX):=\int_0^L\overline{e_n(t)}\,dX_t\) with respect to a CONS \((e_n)_{n\in \mathbb{N}}\) of \(L^2([0,L];\mathbb{C})\). This problem was proposed
by \textit{S. Ogawa} [Stochastics 85, No. 2, 286--294 (2013; Zbl 1292.60056)] and has been studied
by \textit{S. Ogawa} [Sankhyā, Ser. A 77, No. 1, 30--45 (2015; Zbl 1321.60116); Sankhyā, Ser. A 80, 267--279 (2018; \url{doi:10.1007/s13171-018-0128-8})] and
\textit{S. Ogawa} and \textit{H. Uemura} [J. Theor. Probab. 27, No. 2, 370--382 (2014; Zbl 1296.60141); Bull. Sci. Math. 138, No. 1, 147--163 (2014; Zbl 1294.60079); ``On the identification of noncausal functions from the SFCs (symposium on probability theory)'', RIMS Kôkyûroku 1952, 128--134 (2015); Japan J. Ind. Appl. Math. 35, No. 1, 373--390 (2018; Zbl 1390.60194)].
In this paper we give several results on the problem for each of stochastic differentials of Ogawa type and Skorokhod type when \([0, L]\) is a finite or an infinite interval. Specifically, we first give a condition for a random function to be determined from the SFCs and apply it to obtain affirmative answers to the question with several concrete derivation formulas of the random functions.The limiting behavior of some infinitely divisible exponential dispersion models.https://www.zbmath.org/1456.620262021-04-16T16:22:00+00:00"Bar-Lev, Shaul K."https://www.zbmath.org/authors/?q=ai:bar-lev.shaul-k"Letac, Gérard"https://www.zbmath.org/authors/?q=ai:letac.gerard-g(no abstract)Evolutionary dynamics and statistical physics.https://www.zbmath.org/1456.920012021-04-16T16:22:00+00:00"Fisher, Daniel"https://www.zbmath.org/authors/?q=ai:fisher.daniel-s|fisher.daniel-s.1"Lässig, Michael"https://www.zbmath.org/authors/?q=ai:lassig.michael"Shraiman, Boris"https://www.zbmath.org/authors/?q=ai:shraiman.boris-iA continuous updating rule for imprecise probabilities.https://www.zbmath.org/1456.681932021-04-16T16:22:00+00:00"Cattaneo, Marco E. G. V."https://www.zbmath.org/authors/?q=ai:cattaneo.marco-e-g-vSummary: The paper studies the continuity of rules for updating imprecise probability models when new data are observed. Discontinuities can lead to robustness issues: this is the case for the usual updating rules of the theory of imprecise probabilities. An alternative, continuous updating rule is introduced.
For the entire collection see [Zbl 1385.68008].Records in a changing world.https://www.zbmath.org/1456.600492021-04-16T16:22:00+00:00"Krug, Joachim"https://www.zbmath.org/authors/?q=ai:krug.joachimBook review of: M. Baron, Probability and statistics for computer scientists.https://www.zbmath.org/1456.000082021-04-16T16:22:00+00:00"Bakouch, Hasssan S."https://www.zbmath.org/authors/?q=ai:bakouch.hasssan-s"Bakouch, Adel S."https://www.zbmath.org/authors/?q=ai:bakouch.adel-sReview of [Zbl 1122.60001].Hidden Markov models for multivariate functional data.https://www.zbmath.org/1456.623222021-04-16T16:22:00+00:00"Martino, Andrea"https://www.zbmath.org/authors/?q=ai:martino.andrea"Guatteri, Giuseppina"https://www.zbmath.org/authors/?q=ai:guatteri.giuseppina"Paganoni, Anna Maria"https://www.zbmath.org/authors/?q=ai:paganoni.anna-mariaSummary: In this paper we extend the usual Hidden Markov Models framework, where the observed objects are univariate or multivariate data, to the case of functional data, by modeling the temporal structure of a system of multivariate curves evolving in time.Limit theorems for some time-dependent expanding dynamical systems.https://www.zbmath.org/1456.370072021-04-16T16:22:00+00:00"Hafouta, Yeor"https://www.zbmath.org/authors/?q=ai:hafouta.yeorThe author proves several probabilistic limit theorems for some classes of distance expanding sequential dynamical systems. The growth rate of the variances of the underlying partial sums is well understood in the random dynamics setup, where the maps are stationary, but not in the present setup, where various growth rates may occur.
Reviewer: George Stoica (Saint John)On the empirical process of tempered moving averages.https://www.zbmath.org/1456.621812021-04-16T16:22:00+00:00"Beran, Jan"https://www.zbmath.org/authors/?q=ai:beran.jan"Sabzikar, Farzad"https://www.zbmath.org/authors/?q=ai:sabzikar.farzad"Surgailis, Donatas"https://www.zbmath.org/authors/?q=ai:surgailis.donatas"Telkmann, Klaus"https://www.zbmath.org/authors/?q=ai:telkmann.klausSummary: We consider asymptotic properties of the empirical process of tempered moving average with memory parameter \(d \in [ 0 , 1 \slash 2 )\) and tempering parameter \(\lambda_N \to 0\), centered by the marginal distribution function of the corresponding untempered stationary process. We prove that under long memory \(( 0 < d < 1 \slash 2)\) and strong tempering \(( N \lambda_N \to \infty )\) the above empirical process has a faster rate of convergence than under weak or moderate tempering. Moreover, for \(0 < d < 1 \slash 2\) and \(\lambda_N = o ( N^{- 1 \slash ( 1 - 2 d )} )\) a uniform reduction principle holds and weak convergence to a degenerate Gaussian process is obtained.Bounds on optimal transport maps onto log-concave measures.https://www.zbmath.org/1456.490362021-04-16T16:22:00+00:00"Colombo, Maria"https://www.zbmath.org/authors/?q=ai:colombo.maria"Fathi, Max"https://www.zbmath.org/authors/?q=ai:fathi.maxIn this paper the authors provide quantitative bounds on the regularity of transport maps sending a standard Gaussian distribution onto a \(\log\)-concave probability measures on \(\mathbb{R}^d\).
Caffarelli contraction theorem states that, when the target measure \(\mu\) is uniformly \(\log\)-concave, i.e. \(\mu=e^{-V} \mathrm{d} x\) with \(D^2V \ge \alpha\), the optimal transport map is \(\alpha^{-1/2}\)-Lipschitz continuous.
It is thus evident that such regularity degenerates if \(\mu\) is only \(\log\)-concave, i.e. \(\mu=e^{-V} \mathrm{d} x\) with \(D^2V \ge 0\) only. The first main result deals with this case:
the authors prove the quadratic growth at infinity, i.e.
Theorem.
Let \(\mu\) be a centered, isotropic, \(\log\)-concave probability measure on \(\mathbb{R}^d\). Then there exists a universal numerical constant \(C\) such that the Brenier map sending the standard Gaussiandistribution onto \(\mu\) satisfies
\[|T(x)| \le C(d+|x|^2).\]
If instead we assume that \(\mu\) is centered and satisfies a Gaussian concentration property with constant \(\beta\), then
\[|T(x)| \le 12\beta^{-1/2}(17d+|x|^2)^{1/2}.\]
As the authors noted, the left hand side behaves like \( d^{1/2}\), while the right hand side scales like \(d\), thus the above estimates are a bit off-average.
The second result proves some a priori regularity estimates on derivatives of \(T\). The strategy is to revisit Kolesnikov's proof of Sobolev estimates in the uniformly \(\log\)-concave case, to allow for non-uniform lower bounds on the Hessian of the potential. More precisely, the authors obtain the following bound:
Theorem.
Let \(T = \nabla\varphi\) be the Brenier map sending the standard Gaussian measure onto \(\mu = e^{-V} \mathrm{d} x\). Assume that \(\mu\) is centered, isotropic, and that for all \(x\in \mathbb{R}^d\)
\[ c_1 Id \ge D^2 V(x) \ge \frac{c_2}{d+|x|}Id \]
for some \(c_1,c_2>0\). Then
\[ \Big\| \frac{\partial_{ee}^2\varphi}{\sqrt{d+|x|^2}} \Big\|_{p+2,\gamma} \le \frac{C}{c_2} \Big(1+p\frac{\sqrt{c_1}}{4\sqrt{d}}\Big). \]
That is, the authors obtain a bound of the form
\[\partial_{ee}^2\varphi \le Cr \sqrt{d+|x|^2}\]
on the complement of a set with very small Gaussian measure.
Finally, in the spirit of the Caffarelli contraction theorem, the authors obtain a bound on the growth of the eigenvalues in \(L^\infty\):
Theorem.
Let \(T = \nabla\varphi\) be the Brenier map sending the standard Gaussian measure onto \(\mu = e^{-V} \mathrm{d} x\). Assume that \(\mu\) is centered, isotropic, and that for all \(x\in \mathbb{R}^d\)
\[ c_1 Id \ge D^2 V(x) \ge \frac{c_2}{d+|x|}Id \]
for some \(c_1,c_2>0\). Then
\[\|\nabla T(x)\|_{op} \le \max\Big(C\frac{c_1^2}{c_2^2},1\Big)(d+|x|^2)^2. \]
If moreover
\[c_3\ge |\nabla V(x)|,\]
then
\[\|\nabla T(x)\|_{op} \le \max\Big(C\frac{c_1^2}{c_2^2},1\Big)(d^{4/3}+|x|^2). \]
Reviewer: Xin Yang Lu (Thunder Bay)Gibbs state uniqueness for an anharmonic quantum crystal with a non-polynomial double-well potential.https://www.zbmath.org/1456.820712021-04-16T16:22:00+00:00"Rebenko, Alexei L."https://www.zbmath.org/authors/?q=ai:rebenko.alexei-l"Zagrebnov, Valentin A."https://www.zbmath.org/authors/?q=ai:zagrebnov.valentin-aCompact smallest eigenvalue expressions in Wishart-Laguerre ensembles with or without a fixed trace.https://www.zbmath.org/1456.600122021-04-16T16:22:00+00:00"Akemann, Gernot"https://www.zbmath.org/authors/?q=ai:akemann.gernot"Vivo, Pierpaolo"https://www.zbmath.org/authors/?q=ai:vivo.pierpaoloNon-regular \(g\)-measures and variable length memory chains.https://www.zbmath.org/1456.600792021-04-16T16:22:00+00:00"Ferreira, Ricardo F."https://www.zbmath.org/authors/?q=ai:ferreira.ricardo-f"Gallo, Sandro"https://www.zbmath.org/authors/?q=ai:gallo.sandro"Paccaut, Frédéric"https://www.zbmath.org/authors/?q=ai:paccaut.fredericFiltration shrinkage, the structure of deflators, and failure of market completeness.https://www.zbmath.org/1456.600992021-04-16T16:22:00+00:00"Kardaras, Constantinos"https://www.zbmath.org/authors/?q=ai:kardaras.constantinos"Ruf, Johannes"https://www.zbmath.org/authors/?q=ai:ruf.johannesSummary: We analyse the structure of local martingale deflators projected on smaller filtrations. In a general continuous-path setting, we show that the local martingale parts in the multiplicative Doob-Meyer decomposition of projected local martingale deflators are themselves local martingale deflators in the smaller information market. Via use of a Bayesian filtering approach, we demonstrate the exact mechanism of how updates on the possible class of models under less information result in the strict supermartingale property of projections of such deflators. Finally, we demonstrate that these projections are unable to span all possible local martingale deflators in the smaller information market, by investigating a situation where market completeness is not retained under filtration shrinkage.Lack-of-fit of a parametric measurement error AR(1) model.https://www.zbmath.org/1456.621782021-04-16T16:22:00+00:00"Balakrishna, N."https://www.zbmath.org/authors/?q=ai:balakrishna.naveen|balakrishna.narayana"Kim, Jiwoong"https://www.zbmath.org/authors/?q=ai:kim.jiwoong"Koul, Hira L."https://www.zbmath.org/authors/?q=ai:koul.hira-lalSummary: This paper proposes an asymptotically distribution free test for fitting a parametric model to the autoregressive function in the AR(1) model in the presence of measurement error. The test is based on a martingale transform of a certain marked residual empirical process. A simulation study assessing the finite sample level and power performance of the proposed test is also included.Fusion algebra of critical percolation.https://www.zbmath.org/1456.812182021-04-16T16:22:00+00:00"Rasmussen, Jørgen"https://www.zbmath.org/authors/?q=ai:rasmussen.jorgen|rasmussen.jorgen-born|rasmussen.jorgen-h"Pearce, Paul A."https://www.zbmath.org/authors/?q=ai:pearce.paul-aThe Jarzynski relation, fluctuation theorems, and stochastic thermodynamics for non-Markovian processes.https://www.zbmath.org/1456.825712021-04-16T16:22:00+00:00"Speck, T."https://www.zbmath.org/authors/?q=ai:speck.thomas"Seifert, U."https://www.zbmath.org/authors/?q=ai:seifert.udoOn the mean Euler characteristic and mean Betti's numbers of the Ising model with arbitrary spin.https://www.zbmath.org/1456.829702021-04-16T16:22:00+00:00"Blanchard, Philippe"https://www.zbmath.org/authors/?q=ai:blanchard.philippe"Dobrovolny, Christophe"https://www.zbmath.org/authors/?q=ai:dobrovolny.christophe"Gandolfo, Daniel"https://www.zbmath.org/authors/?q=ai:gandolfo.daniel"Ruiz, Jean"https://www.zbmath.org/authors/?q=ai:ruiz.jeanCentral limit theorems for Diophantine approximants.https://www.zbmath.org/1456.111432021-04-16T16:22:00+00:00"Björklund, Michael"https://www.zbmath.org/authors/?q=ai:bjorklund.michael"Gorodnik, Alexander"https://www.zbmath.org/authors/?q=ai:gorodnik.alexanderIn the present paper, the authors prove a central limit theorem for a counting function for the number of solutions to certain Diophantine inequalities. Concretely, let \(\Vert \cdot \Vert\) be some norm on \(\mathbb{R}^n\), let \(\vartheta_1, \dots, \vartheta_m > 0\) and let \(w_1, \dots w_m > 0\) with \(w_1 + \cdots + w_m = n\). For an \(m \times n\) matrix \(u\) with entries in \([0,1]\), let \(L_u^{(i)}\) denote the linear form on \(\mathbb{R}^n\) with coefficients from the \(i\)'th row of \(u\) and consider the system of Diophantine inequalities
\[
\big\vert p_i + L_u^{(i)}(q_1, \dots q_n)\big\vert < \vartheta_i \Vert q \Vert^{-w_i}, \quad i = 1,\dots, m,
\]
with \((p,q) = (p_1, \dots, p_m, q_1, \dots, q_n) \in\mathbb{Z}^m \times (\mathbb{Z}^n\setminus \{0\})\). The authors consider the counting function \(\Delta_T(u)\), which counts the number of solutions to this system of inequalities with \(0 < \Vert q \Vert < T\).
It is shown that the function \(\Delta_T(u)\) satisfies a central limit theorem. Namely, if \(m \ge 2\), \(C_{m,n} = 2^m \vartheta_1 \cdots \vartheta_m \int_{S^{n-1}} \Vert z \Vert^{-n}dz\) and \(\xi \in\mathbb{R}\),
\[
\bigg\vert \bigg\{ u \in M_{m,n}([0,1]):\frac{\Delta_T(u) - C_{m,n}\log T}{(\log T)^{1/2}}< \xi \bigg\}\bigg\vert \longrightarrow \mathrm{Norm}_{\sigma_{m,n}}(\xi),
\]
where \(\sigma_{m,n} = 2 C_{m,n}(2 \zeta(m+n-1)\zeta(m+n)^{-1}-1)\) with \(\zeta\) denoting the Riemann \(\zeta\)-function, and with \(\mathrm{Norm}_\sigma(\xi)\) denoting the distribution function of the usual normal distribution with variance \(\sigma\), i.e.
\[
\mathrm{Norm}_\sigma(\xi) = (2 \pi \sigma)^{-1/2} \int_{-\infty}^{\xi} e^{-s^2/(2\sigma)} ds.
\]
The main result of the paper generalises an earlier result of \textit{D. Dolgopyat} et al. [J. Éc. Polytech., Math. 4, 1--35 (2017; Zbl 1387.60046)], who proved the result with \(w_i = n/m\) for all \(i = 1, \dots, m\). In the preceding paper, this assumption is critical, and to overcome this obstacle, the authors of the present paper conduct a quantitative study of higher order correlations of functions on spaces of unimodular lattices and develop new methods for estimating cumulants of Siegel transforms.
Reviewer: Simon Kristensen (Aarhus)Clustering of extreme events in time series generated by the fractional Ornstein-Uhlenbeck equation.https://www.zbmath.org/1456.622212021-04-16T16:22:00+00:00"Telesca, Luciano"https://www.zbmath.org/authors/?q=ai:telesca.luciano"Czechowski, Zbigniew"https://www.zbmath.org/authors/?q=ai:czechowski.zbigniew.1Summary: We analyze the time clustering phenomenon in sequences of extremes of time series generated by the fractional Ornstein-Uhlenbeck (fO-U) equation as the source of long-term correlation. We used the percentile-based definition of extremes based on the crossing theory or run theory, where a \textit{run} is a sequence of \(L\) contiguous values above a given percentile. Thus, a sequence of extremes becomes a point process in time, being the time of occurrence of the extreme the starting time of the run. We investigate the relationship between the Hurst exponent related to the time series generated by the fO-U equation and three measures of time clustering of the corresponding extremes defined on the base of the 95th percentile. Our results suggest that for persistent pure fractional Gaussian noise, the sequence of the extremes is clusterized, while extremes obtained by antipersistent or Markovian pure fractional Gaussian noise seem to behave more regularly or Poissonianly. However, for the fractional Ornstein-Uhlenbeck equation, the clustering of extremes is evident even for antipersistent and Markovian cases. This is a result of short range correlations caused by differential and drift terms. The drift parameter influences the extremes clustering effect -- it drops with increasing value of the parameter.
{\copyright 2020 American Institute of Physics}On the role of zealotry in the voter model.https://www.zbmath.org/1456.910472021-04-16T16:22:00+00:00"Mobilia, M."https://www.zbmath.org/authors/?q=ai:mobilia.mauro"Petersen, A."https://www.zbmath.org/authors/?q=ai:petersen.anna-katinka|petersen.ashley|petersen.antje|petersen.allan|petersen.anne-c|petersen.aage|petersen.alexander-m"Redner, S."https://www.zbmath.org/authors/?q=ai:redner.sidneyPhase transition in the two-component symmetric exclusion process with open boundaries.https://www.zbmath.org/1456.827262021-04-16T16:22:00+00:00"Brzank, A."https://www.zbmath.org/authors/?q=ai:brzank.a"Schütz, G. M."https://www.zbmath.org/authors/?q=ai:schutz.gunter-mMolecular spiders in one dimension.https://www.zbmath.org/1456.920522021-04-16T16:22:00+00:00"Antal, Tibor"https://www.zbmath.org/authors/?q=ai:antal.tibor"Krapivsky, P. L."https://www.zbmath.org/authors/?q=ai:krapivsky.pavel-l"Mallick, Kirone"https://www.zbmath.org/authors/?q=ai:mallick.kironeCollective behavior and stochastic resonance in a linear underdamped coupled system with multiplicative dichotomous noise and periodical driving.https://www.zbmath.org/1456.340672021-04-16T16:22:00+00:00"Li, Pengfei"https://www.zbmath.org/authors/?q=ai:li.pengfei"Ren, Ruibin"https://www.zbmath.org/authors/?q=ai:ren.ruibin"Fan, Zening"https://www.zbmath.org/authors/?q=ai:fan.zening"Luo, Maokang"https://www.zbmath.org/authors/?q=ai:luo.maokang"Deng, Ke"https://www.zbmath.org/authors/?q=ai:deng.keForward-backward SDEs with jumps and classical solutions to nonlocal quasilinear parabolic PDEs.https://www.zbmath.org/1456.601622021-04-16T16:22:00+00:00"Shamarova, Evelina"https://www.zbmath.org/authors/?q=ai:shamarova.evelina"Sá Pereira, Rui"https://www.zbmath.org/authors/?q=ai:sa-pereira.ruiSummary: We obtain an existence and uniqueness theorem for fully coupled forward-backward SDEs (FBSDEs) with jumps via the classical solution to the associated quasilinear parabolic partial integro-differential equation (PIDE), and provide the explicit form of the FBSDE solution. Moreover, we embed the associated PIDE into a suitable class of non-local quasilinear parabolic PDEs which allows us to extend the methodology of \textit{O. A. Ladyzhenskaya} et al. [Linear and quasi-linear equations of parabolic type. Translated from the Russian by S. Smith. American Mathematical Society (AMS), Providence, RI (1968; Zbl 0174.15403)] to non-local PDEs of this class. Namely, we obtain the existence and uniqueness of a classical solution to both the Cauchy problem and the initial-boundary value problem for non-local quasilinear parabolic second-order PDEs.A relativistically covariant random walk.https://www.zbmath.org/1456.828282021-04-16T16:22:00+00:00"Almaguer, J."https://www.zbmath.org/authors/?q=ai:almaguer.juan-antonio"Larralde, H."https://www.zbmath.org/authors/?q=ai:larralde.hernanDeterminant solution for the totally asymmetric exclusion process with parallel update. II: Ring geometry.https://www.zbmath.org/1456.827102021-04-16T16:22:00+00:00"Povolotsky, A. M."https://www.zbmath.org/authors/?q=ai:povolotsky.a-m"Priezzhev, V. B."https://www.zbmath.org/authors/?q=ai:priezzhev.vyacheslav-borisovichA simple derivation of the Tracy-Widom distribution of the maximal eigenvalue of a Gaussian unitary random matrix.https://www.zbmath.org/1456.600252021-04-16T16:22:00+00:00"Nadal, Celine"https://www.zbmath.org/authors/?q=ai:nadal.celine"Majumdar, Satya N."https://www.zbmath.org/authors/?q=ai:majumdar.satya-nDiffusion processes on small-world networks with distance dependent random links.https://www.zbmath.org/1456.828672021-04-16T16:22:00+00:00"Kozma, Balázs"https://www.zbmath.org/authors/?q=ai:kozma.balazs"Hastings, Matthew B."https://www.zbmath.org/authors/?q=ai:hastings.matthew-b"Korniss, G."https://www.zbmath.org/authors/?q=ai:korniss.gyorgyLimiting laws for divergent spiked eigenvalues and largest nonspiked eigenvalue of sample covariance matrices.https://www.zbmath.org/1456.621132021-04-16T16:22:00+00:00"Cai, T. Tony"https://www.zbmath.org/authors/?q=ai:cai.tianwen-tony|cai.tony-tony"Han, Xiao"https://www.zbmath.org/authors/?q=ai:han.xiao"Pan, Guangming"https://www.zbmath.org/authors/?q=ai:pan.guangmingLet \(\mathbf{Y}=\mathbf{\Gamma X}\) be the data matrix, where \(\mathbf{X}\) be a \((p+l)\times n\) random matrix whose entries are independent with mean means and unit variances and \(\mathbf{\Gamma}\) is a \(p\times(p+l)\) deterministic matrix under condition \(l/p\rightarrow0\). Let \(\mathbf{\Sigma}=\mathbf{\Gamma}\mathbf{\Gamma}^\intercal\) be the population covariance matrix. The sample covariance matrix in such a case is
\[
S_n=\frac{1}{n}\mathbf{Y}\mathbf{Y}^\intercal=\frac{1}{n}\mathbf{\Gamma X}\mathbf{X}^\intercal\mathbf{\Gamma}^\intercal.
\]
Let \(\mathbf{V}\mathbf{\Lambda}^{1/2}\mathbf{U}\) denote the singular value decomposition of matrix \(\mathbf{\Gamma}\), where \(\mathbf{V}\) and \(\mathbf{U}\) are orthogonal matrices and \(\mathbf{\Lambda}\) is a diagonal matrix consisting in descending order eigenvalues \(\mu_1\geqslant\mu_2\geqslant\ldots\geqslant\mu_p\) of matrix \(\mathbf{\Sigma}\).
Authors of the paper suppose that there are \(K\) spiked eigenvalues that are separated from the rest. They assume that eigenvalues \(\mu_1\geqslant\ldots\geqslant\mu_K\) tends to infinity, while the other eigenvalues \( \mu_{K+1}\geqslant\ldots\geqslant\mu_p\) are bounded.
In the paper, the asymptotic behaviour is considered of the spiked eigenvalues and the largest non-spiked eigenvalue. The limiting normal distribution for the spiked sample eigenvalues is established. The limiting \textit{Tracy-Widom} law for the largest non-spiked eigenvalues is obtained. Estimation of the number of spikes and the convergence of the leading eigenvectors are considered.
Reviewer: Jonas Šiaulys (Vilnius)Long and short time asymptotics of the two-time distribution in local random growth.https://www.zbmath.org/1456.824672021-04-16T16:22:00+00:00"Johansson, Kurt"https://www.zbmath.org/authors/?q=ai:johansson.kurtSummary: The two-time distribution gives the limiting joint distribution of the heights at two different times of a local 1D random growth model in the curved geometry. This distribution has been computed in a specific model but is expected to be universal in the KPZ universality class. Its marginals are the GUE Tracy-Widom distribution. In this paper we study two limits of the two-time distribution. The first, is the limit of long time separation when the quotient of the two times goes to infinity, and the second, is the short time limit when the quotient goes to zero.Functional data analysis in the Banach space of continuous functions.https://www.zbmath.org/1456.620852021-04-16T16:22:00+00:00"Dette, Holger"https://www.zbmath.org/authors/?q=ai:dette.holger"Kokot, Kevin"https://www.zbmath.org/authors/?q=ai:kokot.kevin"Aue, Alexander"https://www.zbmath.org/authors/?q=ai:aue.alexanderThe paper develops data analysis methodology for functional time series in the space of all continuous functions because, according to the authors, all functions utilized for practical purpose are continuous. The paper consists of five sections. In the second section, authors of the paper provide some basic facts about \textit{Central Limit Theorem }and \textit{Invariance Principle} for \(C(T)\)-valued random variables, where \(C(T)\) is the set of continuous functions from \(T\) into real line \(\mathbb{R}\).
The third section deals with the two sample problem on the space \(C([0,1])\). Let \(\{X_1,\ldots,X_m\}\) and \(\{Y_1,\ldots,Y_n\}\) be two independent samples of \(C([0,1])\)-valued random variables. Under suitable assumptions expectation functions \(\mu_1=\mathbb{E}X_1\) and \(\mu_2=\mathbb{E}Y_1\) exist together with the covariance kernels. The authors of the paper consider properties of the maximal deviation between two mean curves \[d_\infty=\|\mu_1-\mu_2\|=\sup_{t\in[0,1]}|\mu_1(t)-\mu_2(t)|\]
and provide procedure for testing the hypotheses of relevant difference:
\[
H_0: d_\infty\leqslant \Delta\ \ {\text{versus}}\ \ H_1: d_\infty>\Delta,
\]
where \(\Delta\geqslant 0\) is a constant determined by the user of test.
In the fourth section of the paper, the change point problem is considered. The new results are presented for testing of a change-point for triangular arrays of \(C([0,1])\)-valued random variables satisfying suitable requirements with respect to metric \(\rho(s,t)=|s-t|^\theta\), \(\theta\in(0,1]\).
The simulation study of the derived procedures is described in the last section of the paper.
The detailed proofs of the new results and the detailed simulation study investigating the finite sample properties of the new methodology are given in the supplementary materials \url{doi:10.1214/19-AOS1842SUPPA} and \url{doi:10.1214/19-AOS1842SUPPB}.
Reviewer: Jonas Šiaulys (Vilnius)Boundary value problems and Markov processes. Functional analysis methods for Markov processes. 3rd expanded and revised edition.https://www.zbmath.org/1456.600032021-04-16T16:22:00+00:00"Taira, Kazuaki"https://www.zbmath.org/authors/?q=ai:taira.kazuakiPublisher's description: This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject.
The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
See the reviews of the first and second editions in [Zbl 0766.60097; Zbl 1203.60002].Structure of the stationary state of the asymmetric target process.https://www.zbmath.org/1456.826372021-04-16T16:22:00+00:00"Luck, J. M."https://www.zbmath.org/authors/?q=ai:luck.jean-marc"Godrèche, C."https://www.zbmath.org/authors/?q=ai:godreche.claudeThe one-dimensional KPZ equation and the Airy process.https://www.zbmath.org/1456.827112021-04-16T16:22:00+00:00"Prolhac, Sylvain"https://www.zbmath.org/authors/?q=ai:prolhac.sylvain"Spohn, Herbert"https://www.zbmath.org/authors/?q=ai:spohn.herbertWell-posedness for Hardy-Hénon parabolic equations with fractional Brownian noise.https://www.zbmath.org/1456.601602021-04-16T16:22:00+00:00"Majdoub, Mohamed"https://www.zbmath.org/authors/?q=ai:majdoub.mohamed"Mliki, Ezzedine"https://www.zbmath.org/authors/?q=ai:mliki.ezzedineThe local solvability of Hardy-Hénon parabolic equations in \(\mathbb{R}^N\) (\(N=2,3\)) perturbed by fractional Brownian noise is discussed in this work. The local pathwise existence and uniqueness of a mild \(\mathbb{L}^q\)-solution under suitable assumptions on \(q\) is established using the contraction mapping principle.
Reviewer: Manil T. Mohan (Roorkee)Multi-point distribution function for the continuous time random walk.https://www.zbmath.org/1456.826462021-04-16T16:22:00+00:00"Barkai, E."https://www.zbmath.org/authors/?q=ai:barkai.edi|barkai.eli"Sokolov, I. M."https://www.zbmath.org/authors/?q=ai:sokolov.igor-mikhailovichPhase transitions in the two-species totally asymmetric exclusion process with open boundaries.https://www.zbmath.org/1456.826412021-04-16T16:22:00+00:00"Arita, Chikashi"https://www.zbmath.org/authors/?q=ai:arita.chikashiIsing spin glass models versus Ising models: an effective mapping at high temperature. II: Applications to graphs and networks.https://www.zbmath.org/1456.824732021-04-16T16:22:00+00:00"Ostilli, Massimo"https://www.zbmath.org/authors/?q=ai:ostilli.massimoNon-equilibrium steady states: fluctuations and large deviations of the density and of the current.https://www.zbmath.org/1456.825512021-04-16T16:22:00+00:00"Derrida, Bernard"https://www.zbmath.org/authors/?q=ai:derrida.bernardHolomorphic parafermions in the Potts model and stochastic Loewner evolution.https://www.zbmath.org/1456.821762021-04-16T16:22:00+00:00"Riva, V."https://www.zbmath.org/authors/?q=ai:riva.valentina"Cardy, J."https://www.zbmath.org/authors/?q=ai:cardy.john-lStochastic interacting particle systems out of equilibrium.https://www.zbmath.org/1456.826492021-04-16T16:22:00+00:00"Bertini, L."https://www.zbmath.org/authors/?q=ai:bertini.lorenzo-bertini"De Sole, A."https://www.zbmath.org/authors/?q=ai:de-sole.alberto"Gabrielli, D."https://www.zbmath.org/authors/?q=ai:gabrielli.davide"Jona-Lasinio, G."https://www.zbmath.org/authors/?q=ai:jona-lasinio.giovanni"Landim, C."https://www.zbmath.org/authors/?q=ai:landim.claudioTightness for the minimal displacement of branching random walk.https://www.zbmath.org/1456.602262021-04-16T16:22:00+00:00"Bramson, Maury"https://www.zbmath.org/authors/?q=ai:bramson.maury-d"Zeitouni, Ofer"https://www.zbmath.org/authors/?q=ai:zeitouni.oferRegularly varying random fields.https://www.zbmath.org/1456.601272021-04-16T16:22:00+00:00"Wu, Lifan"https://www.zbmath.org/authors/?q=ai:wu.lifan"Samorodnitsky, Gennady"https://www.zbmath.org/authors/?q=ai:samorodnitsky.gennady-pSummary: We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of \textit{B. Basrak} and \textit{J. Segers} [Stochastic Processes Appl. 119, No. 4, 1055--1080 (2009; Zbl 1161.60319)]. The spatial context requires multiple notions of extremal index, and the tail and spectral fields are applied to clarify these notions and other aspects of extremal clusters. An important application of the techniques we develop is to the Brown-Resnick random fields.Fluctuations of the one-dimensional asymmetric exclusion process using random matrix techniques.https://www.zbmath.org/1456.828382021-04-16T16:22:00+00:00"Sasamoto, T."https://www.zbmath.org/authors/?q=ai:sasamoto.tomohiroEstimates on the tail probabilities of subordinators and applications to general time fractional equations.https://www.zbmath.org/1456.601182021-04-16T16:22:00+00:00"Cho, Soobin"https://www.zbmath.org/authors/?q=ai:cho.soobin"Kim, Panki"https://www.zbmath.org/authors/?q=ai:kim.pankiSummary: In this paper, we study estimates on tail probabilities of several classes of subordinators under mild assumptions on the tails of their Lévy measures. As an application of that result, we obtain two-sided estimates for fundamental solutions of general homogeneous time fractional equations including those with Dirichlet boundary conditions.A slow-to-start traffic model related to a M/M/1 queue.https://www.zbmath.org/1456.900542021-04-16T16:22:00+00:00"Cáceres, Fredy Castellares"https://www.zbmath.org/authors/?q=ai:caceres.fredy-castellares"Ferrari, Pablo A."https://www.zbmath.org/authors/?q=ai:ferrari.pablo-augusto"Pechersky, Eugene"https://www.zbmath.org/authors/?q=ai:pechersky.eugene-aOn a maximal inequality and its application to SDEs with singular drift.https://www.zbmath.org/1456.600562021-04-16T16:22:00+00:00"Liu, Xuan"https://www.zbmath.org/authors/?q=ai:liu.xuan"Xi, Guangyu"https://www.zbmath.org/authors/?q=ai:xi.guangyuSummary: In this paper we present a Doob type maximal inequality for stochastic processes satisfying the conditional increment control condition. If we assume, in addition, that the margins of the process have uniform exponential tail decay, we prove that the supremum of the process decays exponentially in the same manner. Then we apply this result to the construction of the almost everywhere stochastic flow to stochastic differential equations with singular time dependent divergence-free drift.Anisotropic scaling limits of long-range dependent random fields.https://www.zbmath.org/1456.601232021-04-16T16:22:00+00:00"Surgailis, Donatas"https://www.zbmath.org/authors/?q=ai:surgailis.donatasSummary: We review recent results on anisotropic scaling limits and the scaling transition for linear and their subordinated nonlinear long-range dependent stationary random fields \(X\) on \(\mathbb{Z}^2\). The scaling limits \({V}_{\gamma}^X\) are taken over rectangles in \(\mathbb{Z}^2\) whose sides increase as \(O( \lambda )\) and \(O(\lambda \gamma \) ) as \(\lambda \rightarrow \infty\) for any fixed \(\gamma > 0\). The scaling transition occurs at \({\gamma}_0^X>0\) provided that \({V}_{\gamma}^X\) are different for \(\gamma >{\gamma}_0^X\) and \(\gamma <{\gamma}_0^X\) and do not depend on \(\gamma\) otherwise.A supercritical series analysis for the generalized contact process with diffusion.https://www.zbmath.org/1456.823482021-04-16T16:22:00+00:00"Dantas, W. G."https://www.zbmath.org/authors/?q=ai:dantas.wellington-g"Stilck, J. F."https://www.zbmath.org/authors/?q=ai:stilck.jurgen-fFluctuating observation time ensembles in the thermodynamics of trajectories.https://www.zbmath.org/1456.825472021-04-16T16:22:00+00:00"Budini, Adrián A."https://www.zbmath.org/authors/?q=ai:budini.adrian-a"Turner, Robert M."https://www.zbmath.org/authors/?q=ai:turner.robert-m"Garrahan, Juan P."https://www.zbmath.org/authors/?q=ai:garrahan.juan-pedroAsymptotics of intersection local time for diffusion processes.https://www.zbmath.org/1456.601952021-04-16T16:22:00+00:00"Dorogovtsev, Andrey"https://www.zbmath.org/authors/?q=ai:dorogovtsev.andrey-a"Izyumtseva, Olga"https://www.zbmath.org/authors/?q=ai:izyumtseva.olgaSummary: In the paper, we investigate the intersection local time for two correlated Brownian motions on the plane that form a diffusion process in \(\mathbb{R}^4\) associated with a divergence-form generator. Using Gaussian heat kernel bounds, we prove the existence of intersection local time for these Brownian motions, obtain estimates of its moments, and establish the law of iterated logarithm for it.Strong existence and higher order Fréchet differentiability of stochastic flows of fractional Brownian motion driven SDEs with singular drift.https://www.zbmath.org/1456.601402021-04-16T16:22:00+00:00"Baños, David"https://www.zbmath.org/authors/?q=ai:banos.david-r"Nilssen, Torstein"https://www.zbmath.org/authors/?q=ai:nilssen.torstein-k"Proske, Frank"https://www.zbmath.org/authors/?q=ai:proske.frank-norbertSummary: In this paper we present a new method for the construction of strong solutions of SDE's with merely integrable drift coefficients driven by a multidimensional fractional Brownian motion with Hurst parameter \(H<\frac{1}{2}\). Furthermore, we prove the rather surprising result of the higher order Fréchet differentiability of stochastic flows of such SDE's in the case of a small Hurst parameter. In establishing these results we use techniques from Malliavin calculus combined with new ideas based on a ``local time variational calculus''. We expect that our general approach can be also applied to the study of certain types of stochastic partial differential equations as e.g. stochastic conservation laws driven by rough paths.The density of critical percolation clusters touching the boundaries of strips and squares.https://www.zbmath.org/1456.824772021-04-16T16:22:00+00:00"Simmons, Jacob J. H."https://www.zbmath.org/authors/?q=ai:simmons.jacob-j-h"Kleban, Peter"https://www.zbmath.org/authors/?q=ai:kleban.peter"Dahlberg, Kevin"https://www.zbmath.org/authors/?q=ai:dahlberg.kevin"Ziff, Robert M."https://www.zbmath.org/authors/?q=ai:ziff.robert-mLaw of two-sided exit by a spectrally positive strictly stable process.https://www.zbmath.org/1456.601132021-04-16T16:22:00+00:00"Chi, Zhiyi"https://www.zbmath.org/authors/?q=ai:chi.zhiyiSummary: For a spectrally positive strictly stable process with index in (1,2), we obtain (i) the sub-probability density of its first exit time from an interval by hitting the interval's lower end before jumping over its upper end, and (ii) the joint distribution of the time, undershoot, and jump of the process when it makes the first exit the other way around. The density of the exit time is expressed in terms of the roots of a Mittag-Leffler function. Some theoretical applications of the results are given.Invariance principles for random walks in cones.https://www.zbmath.org/1456.601032021-04-16T16:22:00+00:00"Duraj, Jetlir"https://www.zbmath.org/authors/?q=ai:duraj.jetlir"Wachtel, Vitali"https://www.zbmath.org/authors/?q=ai:wachtel.vitali-iSummary: We prove invariance principles for a multidimensional random walk conditioned to stay in a cone. Our first result concerns convergence towards the Brownian meander in the cone. Furthermore, we prove functional convergence of \(h\)-transformed random walk to the corresponding \(h\)-transform of the Brownian motion. Finally, we prove an invariance principle for bridges of a random walk in a cone.SDEs with uniform distributions: peacocks, conic martingales and mean reverting uniform diffusions.https://www.zbmath.org/1456.601412021-04-16T16:22:00+00:00"Brigo, Damiano"https://www.zbmath.org/authors/?q=ai:brigo.damiano"Jeanblanc, Monique"https://www.zbmath.org/authors/?q=ai:jeanblanc.monique"Vrins, Frédéric"https://www.zbmath.org/authors/?q=ai:vrins.fredericSummary: Peacocks are increasing processes for the convex order. To any peacock, one can associate martingales with the same marginal laws. We are interested in finding the \textit{diffusion} associated to the \textit{uniform peacock}, i.e., the peacock with uniform law at all times on a time-varying support \([a(t),b(t)]\). Following an idea from \textit{B. Dupire} [``Pricing with a smile'', Risk 7, 18--20 (1994)], \textit{D. B. Madan} and \textit{M. Yor} [Bernoulli 8, No. 4, 509--536 (2002; Zbl 1009.60037)] propose a construction to find a diffusion martingale associated to a Peacock, under the assumption of existence of a solution to a particular stochastic differential equation (SDE). In this paper we study the SDE associated to the uniform Peacock and give sufficient conditions on the (conic) boundary to have a unique strong or weak solution and analyze the local time at the boundary. Eventually, we focus on the \textit{constant support} case. Given that the only uniform martingale with time-independent support seems to be a constant, we consider more general (mean-reverting) diffusions. We prove existence of a solution to the related SDE and derive the moments of transition densities. Limit-laws and ergodic results show that the transition law tends to a uniform distribution.Temporal evolution of the domain structure in a Poisson-Voronoi transformation.https://www.zbmath.org/1456.828582021-04-16T16:22:00+00:00"Pineda, Eloi"https://www.zbmath.org/authors/?q=ai:pineda.eloi"Crespo, Daniel"https://www.zbmath.org/authors/?q=ai:crespo.danielA simplified proof of CLT for convex bodies.https://www.zbmath.org/1456.520042021-04-16T16:22:00+00:00"Fresen, Daniel J."https://www.zbmath.org/authors/?q=ai:fresen.daniel-jSummary: We present a short proof of Klartag's central limit theorem for convex bodies, using only the most classical facts about log-concave functions. An appendix is included where we give the proof that the thin shell implies CLT. The paper is accessible to anyone.Modeling anomalous diffusion by a subordinated fractional Lévy-stable process.https://www.zbmath.org/1456.602782021-04-16T16:22:00+00:00"Teuerle, Marek"https://www.zbmath.org/authors/?q=ai:teuerle.marek-a"Wyłomańska Agnieszka"https://www.zbmath.org/authors/?q=ai:wylomanska-agnieszka."Sikora, Grzegorz"https://www.zbmath.org/authors/?q=ai:sikora.grzegorzReflected quadratic BSDEs driven by \(G\)-Brownian motions.https://www.zbmath.org/1456.601422021-04-16T16:22:00+00:00"Cao, Dong"https://www.zbmath.org/authors/?q=ai:cao.dong"Tang, Shanjian"https://www.zbmath.org/authors/?q=ai:tang.shanjianSummary: In this paper, the authors consider a reflected backward stochastic differential equation driven by a \(G\)-Brownian motion \((G\)-BSDE for short), with the generator growing quadratically in the second unknown. The authors obtain the existence by the penalty method, and some a priori estimates which imply the uniqueness, for solutions of the \(G\)-BSDE. Moreover, focusing their discussion at the Markovian setting, the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.Effects of system parameters on the optimal cost and policy in a class of multidimensional queueing control problems.https://www.zbmath.org/1456.900592021-04-16T16:22:00+00:00"Vercraene, Samuel"https://www.zbmath.org/authors/?q=ai:vercraene.samuel"Gayon, Jean-Philippe"https://www.zbmath.org/authors/?q=ai:gayon.jean-philippe"Karaesmen, Fikri"https://www.zbmath.org/authors/?q=ai:karaesmen.fikriSummary: We consider a class of Markov Decision Processes frequently employed to model queueing and inventory control problems. For these problems, we explore how changes in different system input parameters (transition rates, costs, discount rates etc.) affect the optimal cost and the optimal policy when the state space of the problem is multidimensional. To address a large class of problems, we introduce two generic dynamic programming operators to model different types of controlled events. For these operators, we derive sufficient conditions to propagate monotonicity and supermodularity properties of the value function. These properties allow to predict how changes in system input parameters affect the optimal cost and policy. Finally, we explore the case when several parameters are changed at the same time.
The online appendix is available at \url{https://doi.org/10.1287/opre.2017.1600}.Two-time correlation and occupation time for the Brownian bridge and tied-down renewal processes.https://www.zbmath.org/1456.602102021-04-16T16:22:00+00:00"Godrèche, Claude"https://www.zbmath.org/authors/?q=ai:godreche.claudeMean unknotting times of random knots and embeddings.https://www.zbmath.org/1456.824322021-04-16T16:22:00+00:00"Chan, Yao-Ban"https://www.zbmath.org/authors/?q=ai:chan.yao-ban"Owczarek, Aleksander L."https://www.zbmath.org/authors/?q=ai:owczarek.aleksander-l"Rechnitzer, Andrew"https://www.zbmath.org/authors/?q=ai:rechnitzer.andrew-daniel"Slade, Gordon"https://www.zbmath.org/authors/?q=ai:slade.gordonLifschitz tail for alloy-type models driven by the fractional Laplacian.https://www.zbmath.org/1456.601192021-04-16T16:22:00+00:00"Kaleta, Kamil"https://www.zbmath.org/authors/?q=ai:kaleta.kamil"Pietruska-Pałuba, Katarzyna"https://www.zbmath.org/authors/?q=ai:pietruska-paluba.katarzynaSummary: We establish precise asymptotics near zero of the integrated density of states for the random Schrödinger operators \(( - \Delta )^{\alpha / 2} + V^\omega\) in \(L^2( \mathbb{R}^d)\) for the full range of \(\alpha \in(0, 2]\) and a fairly large class of random nonnegative alloy-type potentials \(V^\omega \). The IDS exhibits the Lifschitz tail singularity. We prove the existence of the limit \[\lim_{\lambda \to 0} \lambda^{d / \alpha} \ln N(\lambda) = - C \omega_d \left( \lambda_d^{( \alpha )} \right)^{d / \alpha},\] with \(C \in(0, \infty]\). The constant \(C\) is finite if and only if the common distribution of the lattice random variables charges \(\{0\}\). In this case, the constant \(C\) is expressed explicitly in terms of this distribution. In the limit formula, \( \lambda_d^{( \alpha )}\) denotes the Dirichlet ground-state eigenvalue of the operator \(( - \Delta )^{\alpha / 2}\) in the unit ball in \(\mathbb{R}^d\), and \(\omega_d\) is the volume of this ball.Stochastic Loewner evolution driven by Lévy processes.https://www.zbmath.org/1456.824472021-04-16T16:22:00+00:00"Rushkin, I."https://www.zbmath.org/authors/?q=ai:rushkin.i"Oikonomou, P."https://www.zbmath.org/authors/?q=ai:oikonomou.p"Kadanoff, L. P."https://www.zbmath.org/authors/?q=ai:kadanoff.leo-p"Gruzberg, I. A."https://www.zbmath.org/authors/?q=ai:gruzberg.ilya-aLimiting distribution of a sequence of functions defined on a Markov chain.https://www.zbmath.org/1456.600612021-04-16T16:22:00+00:00"Kvatadze, Zurab"https://www.zbmath.org/authors/?q=ai:kvatadze.zurab"Kvatadze, Tsiala"https://www.zbmath.org/authors/?q=ai:kvatadze.tsialaSummary: The present article shows the limiting distribution of partial sums of a functional sequence defined on a Markov Chain in case the chain is ergodic, with one class of ergodicity and contains cyclical subclasses.Deformed Cauchy random matrix ensembles and large \(N\) phase transitions.https://www.zbmath.org/1456.813442021-04-16T16:22:00+00:00"Russo, Jorge G."https://www.zbmath.org/authors/?q=ai:russo.jorge-gSummary: We study a new hermitian one-matrix model containing a logarithmic Penner's type term and another term, which can be obtained as a limit from logarithmic terms. For small coupling, the potential has an absolute minimum at the origin, but beyond a certain value of the coupling the potential develops a double well. For a higher critical value of the coupling, the system undergoes a large \(N\) third-order phase transition.Book review of: S. Sullivant, Algebraic statistics.https://www.zbmath.org/1456.000152021-04-16T16:22:00+00:00"Kahle, Thomas"https://www.zbmath.org/authors/?q=ai:kahle.thomasReview of [Zbl 1408.62004].On the martingale decompositions of Gundy, Meyer, and Yoeurp in infinite dimensions.https://www.zbmath.org/1456.601002021-04-16T16:22:00+00:00"Yaroslavtsev, Ivan S."https://www.zbmath.org/authors/?q=ai:yaroslavtsev.ivanIt is proved that \(X\) is a UMD Banach space if and only if every local martingale \(M: {R}_+ \times \Omega \to X\) has a decomposition \(M=M^{c}+M^{q}+M^{a}\), where \(M^{c}\) is a continuous local martingale, \(M^{q}\) is a purely discontinuous quasi-left continuous local martingale and \(M^{a}\) is a purely discontinuous local martingale with accessible jumps. Moreover, the weak type inequalities
\[
\lambda P(N_t^{*}> \lambda) \leq C E(N_t)
\]
are shown in all the three cases \(N=M^{c},M^{q},M^{a}\).
Reviewer: Ferenc Weisz (Budapest)On intermediate level sets of two-dimensional discrete Gaussian free field.https://www.zbmath.org/1456.600822021-04-16T16:22:00+00:00"Biskup, Marek"https://www.zbmath.org/authors/?q=ai:biskup.marek"Louidor, Oren"https://www.zbmath.org/authors/?q=ai:louidor.orenSummary: We consider the discrete Gaussian free field (DGFF) in scaled-up (square-lattice) versions of suitably regular continuum domains \(D\subset\mathbb{C}\) and describe the scaling limit, including local structure, of the level sets at heights growing as a \(\lambda \)-multiple of the height of the absolute maximum, for any \(\lambda\in(0,1)\). We prove that, in the scaling limit, the scaled spatial position of a typical point \(x\) sampled from this level set is distributed according to a Liouville Quantum Gravity (LQG) measure in \(D\) at parameter equal \(\lambda \)-times its critical value, the field value at \(x\) has an exponential intensity measure and the configuration near \(x\) reduced by the value at \(x\) has the law of a pinned DGFF reduced by a suitable multiple of the potential kernel. In particular, the law of the total size of the level set, properly-normalized, converges to that of the total mass of the LQG measure. This sharpens considerably an earlier conclusion by
\textit{O. Daviaud} [Ann. Probab. 34, No. 3, 962--986 (2006; Zbl 1104.60062)].Book review of: G. Aubrun and S. Szarek, Alice and Bob meet Banach: the interface of asymptotic geometric analysis and quantum information theory.https://www.zbmath.org/1456.000092021-04-16T16:22:00+00:00"Brannan, Michael"https://www.zbmath.org/authors/?q=ai:brannan.michaelReview of [Zbl 1402.46001].On the stochastic Dullin-Gottwald-Holm equation: global existence and wave-breaking phenomena.https://www.zbmath.org/1456.601612021-04-16T16:22:00+00:00"Rohde, Christian"https://www.zbmath.org/authors/?q=ai:rohde.christian"Tang, Hao"https://www.zbmath.org/authors/?q=ai:tang.haoSummary: We consider a class of stochastic evolution equations that include in particular the stochastic Camassa-Holm equation. For the initial value problem on a torus, we first establish the local existence and uniqueness of pathwise solutions in the Sobolev spaces \(H^s\) with \(s>3/2\). Then we show that strong enough nonlinear noise can prevent blow-up almost surely. To analyze the effects of weaker noise, we consider a linearly multiplicative noise with non-autonomous pre-factor. Then, we formulate precise conditions on the initial data that lead to global existence of strong solutions or to blow-up. The blow-up occurs as wave breaking. For blow-up with positive probability, we derive lower bounds for these probabilities. Finally, the blow-up rate of these solutions is precisely analyzed.Mean-field treatment of exclusion processes with random-force disorder.https://www.zbmath.org/1456.828512021-04-16T16:22:00+00:00"Juhász, Róbert"https://www.zbmath.org/authors/?q=ai:juhasz.robertA stochastic ordering based on the canonical transformation of skew-normal vectors.https://www.zbmath.org/1456.600462021-04-16T16:22:00+00:00"Arevalillo, Jorge M."https://www.zbmath.org/authors/?q=ai:arevalillo.jorge-m"Navarro, Hilario"https://www.zbmath.org/authors/?q=ai:navarro.hilarioSummary: In this paper, we define a new skewness ordering that enables stochastic comparisons for vectors that follow a multivariate skew-normal distribution. The new ordering is based on the canonical transformation associated with the multivariate skew-normal distribution and on the well-known convex transform order applied to the only skewed component of such canonical transformation. We examine the connection between the proposed ordering and the multivariate convex transform order studied by
\textit{F. Belzunce} et al. [Test 24, No. 4, 813--834 (2015; Zbl 1358.60024)]. Several standard skewness measures like Mardia's and Malkovich-Afifi's indices are revisited and interpreted in connection with the new ordering; we also study its relationship with the J-divergence between skew-normal and normal random vectors and with the \textit{Negentropy}. Some artificial data are used in simulation experiments to illustrate the theoretical discussion; a real data application is provided as well.Statistics of the longest interval in renewal processes.https://www.zbmath.org/1456.602342021-04-16T16:22:00+00:00"Godrèche, Claude"https://www.zbmath.org/authors/?q=ai:godreche.claude"Majumdar, Satya N."https://www.zbmath.org/authors/?q=ai:majumdar.satya-n"Schehr, Grégory"https://www.zbmath.org/authors/?q=ai:schehr.gregoryLarge deviations of the maximal eigenvalue of random matrices.https://www.zbmath.org/1456.600152021-04-16T16:22:00+00:00"Borot, G."https://www.zbmath.org/authors/?q=ai:borot.gaetan"Eynard, B."https://www.zbmath.org/authors/?q=ai:eynard.bertrand"Majumdar, S. N."https://www.zbmath.org/authors/?q=ai:majumdar.satya-n"Nadal, C."https://www.zbmath.org/authors/?q=ai:nadal.celineAnomalous transport in disordered exclusion processes with coupled particles.https://www.zbmath.org/1456.602582021-04-16T16:22:00+00:00"Juhász, Róbert"https://www.zbmath.org/authors/?q=ai:juhasz.robertOn a semilinear double fractional heat equation driven by fractional Brownian sheet.https://www.zbmath.org/1456.601632021-04-16T16:22:00+00:00"Xia, Dengfeng"https://www.zbmath.org/authors/?q=ai:xia.dengfeng"Yan, Litan"https://www.zbmath.org/authors/?q=ai:yan.litan"Yin, Xiuwei"https://www.zbmath.org/authors/?q=ai:yin.xiuweiSummary: In this paper, we consider the stochastic heat equation of the form
\[ \frac{\partial u}{\partial t}=(\Delta_\alpha+\Delta_\beta)u+ \frac{\partial f}{\partial x}(t,x,u)+\frac{\partial^2W}{\partial t\partial x}, \]
where \(1<\beta<\alpha<2\), \(W(t,x)\) is a fractional Brownian sheet, \(\Delta_\theta:=-(-\Delta)^{\theta/2}\) denotes the fractional Lapalacian operator and \(f:[0,T]\times\mathbb{R}\times\mathbb{R}\to\mathbb{R}\) is a nonlinear measurable function. We introduce the existence, uniqueness and Hölder regularity of the solution. As a related question, we consider also a large deviation principle associated with the above equation with a small perturbation via an equivalence relationship between Laplace principle and large deviation principle.The effect of the three-spin interaction and the next nearest neighbor interaction on the quenching dynamics of a transverse Ising model.https://www.zbmath.org/1456.821172021-04-16T16:22:00+00:00"Divakaran, Uma"https://www.zbmath.org/authors/?q=ai:divakaran.uma"Dutta, Amit"https://www.zbmath.org/authors/?q=ai:dutta.amit-kumarA probabilistic proof of a recursion formula for sums of powers.https://www.zbmath.org/1456.600332021-04-16T16:22:00+00:00"Hu, Xibao"https://www.zbmath.org/authors/?q=ai:hu.xibao"Zhong, Yumin"https://www.zbmath.org/authors/?q=ai:zhong.yuminSummary: A probabilistic proof of a recursion formula for sums of powers is given by using some properties of expectations.Dichotomy of iterated means for nonlinear operators.https://www.zbmath.org/1456.470202021-04-16T16:22:00+00:00"Saburov, Mansur"https://www.zbmath.org/authors/?q=ai:saburov.mansur-khSummary: In this paper, we discuss a dichotomy of iterated means of nonlinear operators acting on a compact convex subset of a finite-dimensional real Banach space. As an application, we study the mean ergodicity of nonhomogeneous Markov chains.Some exact results for the exclusion process.https://www.zbmath.org/1456.826782021-04-16T16:22:00+00:00"Mallick, Kirone"https://www.zbmath.org/authors/?q=ai:mallick.kironeLargest Schmidt eigenvalue of random pure states and conductance distribution in chaotic cavities.https://www.zbmath.org/1456.825352021-04-16T16:22:00+00:00"Vivo, Pierpaolo"https://www.zbmath.org/authors/?q=ai:vivo.pierpaoloGeometric ergodicity in a weighted Sobolev space.https://www.zbmath.org/1456.601742021-04-16T16:22:00+00:00"Devraj, Adithya"https://www.zbmath.org/authors/?q=ai:devraj.adithya"Kontoyiannis, Ioannis"https://www.zbmath.org/authors/?q=ai:kontoyiannis.ioannis"Meyn, Sean"https://www.zbmath.org/authors/?q=ai:meyn.sean-pSummary: For a discrete-time Markov chain \(\boldsymbol{X}=\{X(t)\}\) evolving on \(\mathbb{R}^{\ell}\) with transition kernel \(P\), natural, general conditions are developed under which the following are established:
\begin{itemize}
\item[(i)] The transition kernel \(P\) has a purely discrete spectrum, when viewed as a linear operator on a weighted Sobolev space \(L_{\infty}^{v,1}\) of functions with norm, \[ \Vert f\Vert_{v,1}=\mathop{\text{sup}}_{x\in\mathbb{R}^{\ell}}\frac{1}{v(x)}\max\{\vert f(x)\vert ,\vert \partial_1f(x)\vert ,\ldots,\vert \partial_{\ell}f(x)\vert \},\] where \(v\colon\mathbb{R}^{\ell}\to[1,\infty)\) is a Lyapunov function and \(\partial_i:=\partial/\partial x_i \).
\item[(ii)] The Markov chain is geometrically ergodic in \(L_{\infty}^{v,1}\): There is a unique invariant probability measure \(\pi\) and constants \(B<\infty\) and \(\delta>0\) such that, for each \(f\in L_{\infty}^{v,1}\), any initial condition \(X(0)=x\), and all \(t\geq0\): \begin{eqnarray*}\vert \mathsf{E}_x[f(X(t))]-\pi(f)\vert &\le&B\Vert f\Vert_{v,1}e^{-\delta t}v(x),\\\Vert \nabla\mathsf{E}_x[f(X(t))]\Vert_2&\le&B\Vert f\Vert_{v,1}e^{-\delta t}v(x),\end{eqnarray*} where \(\pi(f)=\int f\,d\pi \).
\item[(iii)] For any function \(f\in L_{\infty}^{v,1}\) there is a function \(h\in L_{\infty}^{v,1}\) solving Poisson's equation: \[h-Ph=f-\pi(f)\].
\end{itemize}
Part of the analysis is based on an operator-theoretic treatment of the sensitivity process that appears in the theory of Lyapunov exponents. Relationships with topological coupling, in terms of the Wasserstein metric, are also explored.Mallows permutations and finite dependence.https://www.zbmath.org/1456.600812021-04-16T16:22:00+00:00"Holroyd, Alexander E."https://www.zbmath.org/authors/?q=ai:holroyd.alexander-e"Hutchcroft, Tom"https://www.zbmath.org/authors/?q=ai:hutchcroft.tom"Levy, Avi"https://www.zbmath.org/authors/?q=ai:levy.aviSummary: We use the Mallows permutation model to construct a new family of stationary finitely dependent proper colorings of the integers. We prove that these colorings can be expressed as finitary factors of i.i.d. processes with finite mean coding radii. They are the first colorings known to have these properties. Moreover, we prove that the coding radii have exponential tails, and that the colorings can also be expressed as functions of countable-state Markov chains. We deduce analogous existence statements concerning shifts of finite type and higher-dimensional colorings.Spatial and temporal white noises under sublinear \(G\)-expectation.https://www.zbmath.org/1456.601332021-04-16T16:22:00+00:00"Ji, Xiaojun"https://www.zbmath.org/authors/?q=ai:ji.xiaojun.1|ji.xiaojun"Peng, Shige"https://www.zbmath.org/authors/?q=ai:peng.shigeSummary: Under the framework of sublinear expectation, we introduce a new type of \(G\)-Gaussian random fields, which contains a type of spatial white noise as a special case. Based on this result, we also introduce a spatial-temporal \(G\)-white noise. Different from the case of linear expectation, in which the probability measure needs to be known, under the uncertainty of probability measures, spatial white noises are intrinsically different from temporal cases.A general and solvable random matrix model for spin decoherence.https://www.zbmath.org/1456.824912021-04-16T16:22:00+00:00"David, François"https://www.zbmath.org/authors/?q=ai:david.francoisAsymptotic statistics of the \(n\)-sided planar Poisson-Voronoi cell. II: Heuristics.https://www.zbmath.org/1456.600412021-04-16T16:22:00+00:00"Hilhorst, H. J."https://www.zbmath.org/authors/?q=ai:hilhorst.hendrik-jan\(L^q(L^p)\)-theory of stochastic differential equations.https://www.zbmath.org/1456.601532021-04-16T16:22:00+00:00"Xia, Pengcheng"https://www.zbmath.org/authors/?q=ai:xia.pengcheng"Xie, Longjie"https://www.zbmath.org/authors/?q=ai:xie.longjie"Zhang, Xicheng"https://www.zbmath.org/authors/?q=ai:zhang.xicheng"Zhao, Guohuan"https://www.zbmath.org/authors/?q=ai:zhao.guohuanSummary: In this paper we show the weak differentiability of the unique strong solution with respect to the starting point \(x\) as well as Bismut-Elworthy-Li's derivative formula for the following stochastic differential equation in \(\mathbb{R}^d\):
\[
dX_t = b(t, X_t)dt + \sigma(t, X_t) dW_t, \quad X_0 = x,
\]
where \(\sigma\) is bounded, uniformly continuous and nondegenerate, \(b \in \widetilde{\mathbb{L}}_{q_1}^{p_1}\) and \(\nabla \sigma \in \widetilde{\mathbb{L}}_{q_2}^{p_2}\) for some \(p_i , q_i \in [2 , \infty)\) with \(\frac{d}{p_i} + \frac{2}{ q_i} < 1, i = 1, 2\), where \(\widetilde{\mathbb{L}}_{q_i}^{p_i}, i = 1, 2\) are some localized spaces of \(L^{q_i} (\mathbb{R}_+ ; L^{p_i} (\mathbb{R}^d))\). Moreover, in the endpoint case \(b \in \widetilde{\mathbb{L}}_\infty^{d; \text{uni}} \subset \widetilde{\mathbb{L}}_\infty^d\), we also show the weak well-posedness.On the local space -- time structure of non-equilibrium steady states.https://www.zbmath.org/1456.826242021-04-16T16:22:00+00:00"Lefevere, Raphaël"https://www.zbmath.org/authors/?q=ai:lefevere.raphaelAgeing in the contact process: scaling behaviour and universal features.https://www.zbmath.org/1456.827252021-04-16T16:22:00+00:00"Baumann, Florian"https://www.zbmath.org/authors/?q=ai:baumann.florian"Gambassi, Andrea"https://www.zbmath.org/authors/?q=ai:gambassi.andreaStationary points in coalescing stochastic flows on \(\mathbb{R}\).https://www.zbmath.org/1456.601142021-04-16T16:22:00+00:00"Dorogovtsev, Andrey A."https://www.zbmath.org/authors/?q=ai:dorogovtsev.andrey-a"Riabov, Georgii V."https://www.zbmath.org/authors/?q=ai:riabov.georgii-v"Schmalfuß, Björn"https://www.zbmath.org/authors/?q=ai:schmalfuss.bjornSummary: This work is devoted to long-time properties of the Arratia flow with drift -- a stochastic flow on \(\mathbb{R}\) whose one-point motions are weak solutions to a stochastic differential equation \(dX(t) = a(X(t))dt + dw(t)\) that move independently before the meeting time and coalesce at the meeting time. We study special modification of such flow that gives rise to a random dynamical system and thus allows to discuss stationary points. Existence of a unique stationary point is proved in the case of a strictly monotone Lipschitz drift by developing a variant of a pullback procedure. Connections between the existence of a stationary point and properties of a dual flow are discussed.Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces.https://www.zbmath.org/1456.601222021-04-16T16:22:00+00:00"Cleanthous, Galatia"https://www.zbmath.org/authors/?q=ai:cleanthous.galatia"Georgiadis, Athanasios G."https://www.zbmath.org/authors/?q=ai:georgiadis.athanasios-g"Lang, Annika"https://www.zbmath.org/authors/?q=ai:lang.annika"Porcu, Emilio"https://www.zbmath.org/authors/?q=ai:porcu.emilioSummary: Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided.High excursions of Bessel and related random processes.https://www.zbmath.org/1456.600882021-04-16T16:22:00+00:00"Piterbarg, Vladimir I."https://www.zbmath.org/authors/?q=ai:piterbarg.vladimir-i"Rodionov, Igor V."https://www.zbmath.org/authors/?q=ai:rodionov.i-vSummary: Asymptotic behavior of large excursions probabilities is evaluated for Euclidean norm of a wide class of Gaussian non-stationary vector processes with independent identically distributed components. It is assumed that the components have means zero and variances reaching its absolute maximum at only one point of the considered time interval. The Bessel process is an important example of such processes.The speed of a general random walk reinforced by its recent history.https://www.zbmath.org/1456.601092021-04-16T16:22:00+00:00"Pinsky, Ross G."https://www.zbmath.org/authors/?q=ai:pinsky.ross-gSummary: We consider a class of random walks whose increment distributions depend on the average value of the process over its most recent \(N\) steps. We investigate the speed of the process, and in particular, the limiting speed as the ``history window'' \(N \to \infty\).Malliavin smoothness on the Lévy space with Hölder continuous or \(B V\) functionals.https://www.zbmath.org/1456.601152021-04-16T16:22:00+00:00"Laukkarinen, Eija"https://www.zbmath.org/authors/?q=ai:laukkarinen.eijaSummary: We consider Malliavin smoothness of random variables \(f(X_1)\), where \(X\) is a pure jump Lévy process and the function \(f\) is either bounded and Hölder continuous or of bounded variation. We show that Malliavin differentiability and fractional differentiability of \(f(X_1)\) depend both on the regularity of \(f\) and the Blumenthal-Getoor index of the Lévy measure.Backward stochastic differential equations with two barriers and generalized reflection.https://www.zbmath.org/1456.601442021-04-16T16:22:00+00:00"Falkowski, Adrian"https://www.zbmath.org/authors/?q=ai:falkowski.adrian"Słomiński, Leszek"https://www.zbmath.org/authors/?q=ai:slominski.leszekSummary: We prove the existence and uniqueness of solutions of backward stochastic differential equations (BSDEs) with generalized reflection at time dependent càdlàg barriers. The reflection model we consider includes, as special cases, the standard reflection as well as the mirror reflection studied earlier in the theory of forward stochastic differential equations. We also show that the solution of BSDEs with generalized reflection corresponds to the value of an optimal stopping problem.Large deviations for correlated random variables described by a matrix product ansatz.https://www.zbmath.org/1456.600622021-04-16T16:22:00+00:00"Angeletti, Florian"https://www.zbmath.org/authors/?q=ai:angeletti.florian"Touchette, Hugo"https://www.zbmath.org/authors/?q=ai:touchette.hugo"Bertin, Eric"https://www.zbmath.org/authors/?q=ai:bertin.eric-m"Abry, Patrice"https://www.zbmath.org/authors/?q=ai:abry.patriceSubcritical branching processes in random environment with immigration: survival of a single family.https://www.zbmath.org/1456.602282021-04-16T16:22:00+00:00"Vatutin, V. A."https://www.zbmath.org/authors/?q=ai:vatutin.vladimir-a"Dyakonova, E. E."https://www.zbmath.org/authors/?q=ai:dyakonova.e-eGeneralized \(k\)-variations and Hurst parameter estimation for the fractional wave equation via Malliavin calculus.https://www.zbmath.org/1456.600892021-04-16T16:22:00+00:00"Shevchenko, Radomyra"https://www.zbmath.org/authors/?q=ai:shevchenko.radomyra"Slaoui, Meryem"https://www.zbmath.org/authors/?q=ai:slaoui.meryem"Tudor, C. A."https://www.zbmath.org/authors/?q=ai:tudor.ciprian-aSummary: We analyze the generalized \(k\)-variations for the solution to the wave equation driven by an additive Gaussian noise which behaves as a fractional Brownian motion with Hurst parameter \(H \geq \frac{ 1}{ 2}\) in time and which is white in space. The \(k\)-variations are defined along \textit{filters} of any order \(p \geq 1\) and of any length. We show that the sequence of generalized \(k\)-variations satisfies a central limit theorem when \(p > H + \frac{ 1}{ 4}\) and we estimate the rate of convergence for it via the Stein-Malliavin calculus. The results are applied to the estimation of the Hurst index. We construct several consistent estimators for \(H\) and analyze these estimators theoretically and numerically.A comparison principle for random walk on dynamical percolation.https://www.zbmath.org/1456.602562021-04-16T16:22:00+00:00"Hermon, Jonathan"https://www.zbmath.org/authors/?q=ai:hermon.jonathan"Sousi, Perla"https://www.zbmath.org/authors/?q=ai:sousi.perlaSummary: We consider the model of random walk on dynamical percolation introduced by \textit{Y. Peres} et al. [Probab. Theory Relat. Fields 162, No. 3--4, 487--530 (2015; Zbl 1326.60140)]. We obtain comparison results for this model for hitting and mixing times and for the spectral gap and log-Sobolev constant with the corresponding quantities for simple random walk on the underlying graph \(G\), for general graphs. When \(G\) is the torus \(\mathbb{Z}_n^d\), we recover the results of Peres et al. [loc. cit.], and we also extend them to the critical case. We also obtain bounds in the cases where \(G\) is a transitive graph of moderate growth and also when it is the hypercube.Spectral gaps for reversible Markov processes with chaotic invariant measures: the Kac process with hard sphere collisions in three dimensions.https://www.zbmath.org/1456.602522021-04-16T16:22:00+00:00"Carlen, Eric"https://www.zbmath.org/authors/?q=ai:carlen.eric-anders"Carvalho, Maria"https://www.zbmath.org/authors/?q=ai:carvalho.maria-conceicao"Loss, Michael"https://www.zbmath.org/authors/?q=ai:loss.michael|loss.michael-pSummary: We develop a method for producing estimates on the spectral gaps of reversible Markov jump processes with chaotic invariant measures, that is effective in the case of degenerate jump rates, and we apply it to prove the Kac conjecture for hard sphere collision in three dimensions.Localization in Gaussian disordered systems at low temperature.https://www.zbmath.org/1456.602702021-04-16T16:22:00+00:00"Bates, Erik"https://www.zbmath.org/authors/?q=ai:bates.erik"Chatterjee, Sourav"https://www.zbmath.org/authors/?q=ai:chatterjee.sourav.1Summary: For a broad class of Gaussian disordered systems at low temperature, we show that the Gibbs measure is asymptotically localized in small neighborhoods of a small number of states. From a single argument, we obtain: (i) a version of ``complete'' path localization for directed polymers that is not available even for exactly solvable models, and (ii) a result about the exhaustiveness of Gibbs states in spin glasses not requiring the Ghirlanda-Guerra identities.A Bayesian semiparametric Archimedean copula.https://www.zbmath.org/1456.620532021-04-16T16:22:00+00:00"Hoyos-Argüelles, Ricardo"https://www.zbmath.org/authors/?q=ai:hoyos-arguelles.ricardo"Nieto-Barajas, Luis"https://www.zbmath.org/authors/?q=ai:nieto-barajas.luis-eSummary: An Archimedean copula is characterised by its generator. This is a real function whose inverse behaves as a survival function. We propose a semiparametric generator based on a quadratic spline. This is achieved by modelling the first derivative of a hazard rate function, in a survival analysis context, as a piecewise constant function. Convexity of our semiparametric generator is obtained by imposing some simple constraints. The induced semiparametric Archimedean copula produces Kendall's tau association measure that covers the whole range \((- 1, 1)\). Inference on the model is done under a Bayesian approach and for some prior specifications we are able to perform an independence test. Properties of the model are illustrated with a simulation study as well as with a real dataset.Anisotropic bootstrap percolation in three dimensions.https://www.zbmath.org/1456.602502021-04-16T16:22:00+00:00"Blanquicett, Daniel"https://www.zbmath.org/authors/?q=ai:blanquicett.danielSummary: Consider a \(p\)-random subset \(A\) of initially infected vertices in the discrete cube \([L]^3\), and assume that the neighborhood of each vertex consists of the \(a_i\) nearest neighbors in the \(\pm e_i\)-directions for each \(i \in \{1, 2, 3\}\), where \(a_1 \le a_2 \le a_3\). Suppose we infect any healthy vertex \(x \in [L]^3\) already having \(a_3 + 1\) infected neighbors, and that infected sites remain infected forever. In this paper, we determine the critical length for percolation up to a constant factor in the exponent, for all triples \((a_1, a_2, a_3)\). To do so, we introduce a new algorithm called the \textit{beams process} and prove an exponential decay property for a family of subcritical two-dimensional bootstrap processes.Statistical inferences for price staleness.https://www.zbmath.org/1456.622502021-04-16T16:22:00+00:00"Kolokolov, Aleksey"https://www.zbmath.org/authors/?q=ai:kolokolov.aleksey"Livieri, Giulia"https://www.zbmath.org/authors/?q=ai:livieri.giulia"Pirino, Davide"https://www.zbmath.org/authors/?q=ai:pirino.davideSummary: This paper proposes a nonparametric theory for statistical inferences on zero returns of high-frequency asset prices. Using an infill asymptotic design, we derive limit theorems for the percentage of zero returns observed on a finite time interval and for other related quantities. Within this framework, we develop two nonparametric tests. First, we test whether intra-day zero returns are independent and identically distributed. Second, we test whether intra-day variation of the likelihood of occurrence of zero returns can be solely explained by a deterministic diurnal pattern. In an empirical application to ten representative stocks of the NYSE, we provide evidence that the null of independent and identically distributed intra-day zero returns can be conclusively rejected. We further find that a deterministic diurnal pattern is not sufficient to explain the intra-day variability of the distribution of zero returns.Mixing time of the adjacent walk on the simplex.https://www.zbmath.org/1456.601852021-04-16T16:22:00+00:00"Caputo, Pietro"https://www.zbmath.org/authors/?q=ai:caputo.pietro"Labbé, Cyril"https://www.zbmath.org/authors/?q=ai:labbe.cyril"Lacoin, Hubert"https://www.zbmath.org/authors/?q=ai:lacoin.hubertSummary: By viewing the \(N\)-simplex as the set of positions of \(N - 1\) ordered particles on the unit interval, the adjacent walk is the continuous-time Markov chain obtained by updating independently at rate 1 the position of each particle with a sample from the uniform distribution over the interval given by the two particles adjacent to it. We determine its spectral gap and prove that both the total variation distance and the separation distance to the uniform distribution exhibit a cutoff phenomenon, with mixing times that differ by a factor \(2\). The results are extended to the family of log-concave distributions obtained by replacing the uniform sampling by a symmetric log-concave Beta distribution.Nonlinear large deviation bounds with applications to Wigner matrices and sparse Erdős-Rényi graphs.https://www.zbmath.org/1456.600632021-04-16T16:22:00+00:00"Augeri, Fanny"https://www.zbmath.org/authors/?q=ai:augeri.fannySummary: We prove general nonlinear large deviation estimates similar to Chatterjee-Dembo's original bounds, except that we do not require any second order smoothness. Our approach relies on convex analysis arguments and is valid for a broad class of distributions. Our results are then applied in three different setups. Our first application consists in the mean-field approximation of the partition function of the Ising model under an optimal assumption on the spectra of the adjacency matrices of the sequence of graphs. Next, we apply our general large deviation bound to investigate the large deviation of the traces of powers of Wigner matrices with sub-Gaussian entries and the upper tail of cycles counts in sparse Erdős-Rényi graphs down to the sparsity threshold \(n^{-1/2}\).Anomalous diffusion for multi-dimensional critical kinetic Fokker-Planck equations.https://www.zbmath.org/1456.602762021-04-16T16:22:00+00:00"Fournier, Nicolas"https://www.zbmath.org/authors/?q=ai:fournier.nicolas-g"Tardif, Camille"https://www.zbmath.org/authors/?q=ai:tardif.camilleSummary: We consider a particle moving in \(d \geq 2\) dimensions, its velocity being a reversible diffusion process, with identity diffusion coefficient, of which the invariant measure behaves, roughly, like \((1 + |v|)^{-\beta}\) as \(|v| \to \infty\), for some constant \(\beta > 0\). We prove that for large times, after a suitable rescaling, the position process resembles a Brownian motion if \(\beta \geq 4 + d\), a stable process if \(\beta \in [d, 4 + d)\) and an integrated multi-dimensional generalization of a Bessel process if \(\beta \in (d - 2, d)\). The critical cases \(\beta = d, \beta = 1 + d\) and \(\beta = 4 + d\) require special rescalings.Solution of the Kolmogorov equation for TASEP.https://www.zbmath.org/1456.602632021-04-16T16:22:00+00:00"Nica, Mihai"https://www.zbmath.org/authors/?q=ai:nica.mihai.2|nica.mihai"Quastel, Jeremy"https://www.zbmath.org/authors/?q=ai:quastel.jeremy"Remenik, Daniel"https://www.zbmath.org/authors/?q=ai:remenik.danielSummary: We provide a direct and elementary proof that the formula obtained in [the second author et al., ``The KPZ fixed point'', Preprint, \url{arXiv:1701.00018}] for the TASEP transition probabilities for general (one-sided) initial data solves the Kolmogorov backward equation. The same method yields the solution for the related PushASEP particle system.Flexible multivariate Hill estimators.https://www.zbmath.org/1456.620922021-04-16T16:22:00+00:00"Dominicy, Yves"https://www.zbmath.org/authors/?q=ai:dominicy.yves"Heikkilä, Matias"https://www.zbmath.org/authors/?q=ai:heikkila.matias"Ilmonen, Pauliina"https://www.zbmath.org/authors/?q=ai:ilmonen.pauliina"Veredas, David"https://www.zbmath.org/authors/?q=ai:veredas.davidSummary: \textit{Y. Dominicy} et al. [``Multivariate Hill estimators'', Int. Stat. Rev. 85, No. 1, 108--142 (2017; \url{doi:10.1111/insr.12120})] introduce a family of Hill estimators for elliptically distributed and heavy tailed random vectors. They propose to use the univariate Hill to a norm of order \(h\) of the data. The norms are homogeneous functions of order one. We show that the family of estimators can be generalized to homogeneous functions of any order and, more importantly, that ellipticity is not required. Only multivariate regular variation is needed, as it is preserved under well-behaved homogeneous functions. This enables us to have flexibility in terms of the estimator and the underlying distribution. Consistency and asymptotic normality are shown, and a Monte Carlo study is conducted to assess the finite sample properties under different asymmetric and heavy tailed multivariate distributions. We illustrate the estimators with an application to 10 years of daily data of paid claims from property insurance policies across 15 regions of Belgium.Deterministic walks in random environment.https://www.zbmath.org/1456.602692021-04-16T16:22:00+00:00"Aimino, Romain"https://www.zbmath.org/authors/?q=ai:aimino.romain"Liverani, Carlangelo"https://www.zbmath.org/authors/?q=ai:liverani.carlangeloSummary: Motivated by the random Lorentz gas, we study deterministic walks in random environment and show that (in simple, yet relevant cases) they can be reduced to a class of random walks in random environment where the jump probability depends (weakly) on the past. In addition, we prove few basic results (hopefully, the germ of a general theory) for the latter purely probabilistic model.On the absolute continuity of random nodal volumes.https://www.zbmath.org/1456.601362021-04-16T16:22:00+00:00"Angst, Jürgen"https://www.zbmath.org/authors/?q=ai:angst.jurgen"Poly, Guillaume"https://www.zbmath.org/authors/?q=ai:poly.guillaumeSummary: We study the absolute continuity with respect to the Lebesgue measure of the distribution of the nodal volume associated with a smooth, nondegenerate and stationary Gaussian field \((f(x), x \in \mathbb{R}^d)\). Under mild conditions, we prove that in dimension \(d \geq 3\), the distribution of the nodal volume has an absolutely continuous component plus a possible singular part. This singular part is actually unavoidable bearing in mind that some Gaussian processes have a positive probability to keep a constant sign on some compact domain. Our strategy mainly consists in proving closed Kac-Rice type formulas allowing one to express the volume of the set \(\{f=0\}\) as integrals of explicit functionals of \((f, \nabla f, \text{Hess}(f))\) and next to deduce that the random nodal volume belongs to the domain of a suitable Malliavin gradient. The celebrated Bouleau-Hirsch criterion then gives conditions ensuring the absolute continuity.Identification of the polaron measure in strong coupling and the Pekar variational formula.https://www.zbmath.org/1456.602112021-04-16T16:22:00+00:00"Mukherjee, Chiranjib"https://www.zbmath.org/authors/?q=ai:mukherjee.chiranjib"Varadhan, S. R. S."https://www.zbmath.org/authors/?q=ai:varadhan.s-r-srinivasaSummary: The path measure corresponding to the Fröhlich polaron appearing in quantum statistical mechanics is defined as the tilted measure
\[
\text{d} \widehat{\mathbb{P}}_{\varepsilon, T} = \frac{1}{Z (\varepsilon, T)} \exp\left\{\frac{1}{2} \int\nolimits_{-T}^T \int_{-T}^T \frac{\varepsilon \text{e}^{-\varepsilon |t - s|}}{|\omega (t) - \omega (s)|} \text{d}s \text{d}t\right\} \text{d}\mathbb{P}.
\]
Here, \(\varepsilon > 0\) is a constant known as the Kac parameter or the inverse-coupling parameter, and \(\mathbb{P}\) is the distribution of the increments of the three-dimensional Brownian motion. In [the authors, Commun. Pure Appl. Math. 73, No. 2, 350--383 (2020; Zbl 1442.60082)] it was shown that, when \(\varepsilon > 0\) is sufficiently small or sufficiently large, the (thermodynamic) limit \(\lim_{T \to \infty} \widehat{\mathbb{P}}_{\varepsilon, T} = \widehat{\mathbb{P}}_{\varepsilon}\) exists as a process with stationary increments, and this limit was identified explicitly as a mixture of Gaussian processes. In the present article the \textit{strong coupling limit} or the vanishing Kac parameter limit \(\lim_{\varepsilon \to 0} \widehat{\mathbb{P}}_{\varepsilon}\) is investigated. It is shown that this limit exists and coincides with the increments of the so-called \textit{Pekar process}, a stationary diffusion with generator \(\frac{1}{2} \Delta +(\nabla \psi / \psi) \cdot \nabla\), where \(\psi\) is the unique (up to spatial translations) maximizer of the Pekar variational problem
\[
g_0 = \underset{\| \psi \|_2 = 1}{\text{sup}} \left\{\int\nolimits_{\mathbb{R}^3} \int\nolimits_{\mathbb{R}^3} \psi^2(x) \psi^2(y) |x - y|^{-1} \text{d}x \text{d}y - \frac{1}{2} \|\nabla \psi\|_2^2\right\}.
\]
As the Pekar process was also earlier shown [the authors, Ann. Probab. 44, No. 6, 3934--3964 (2016; Zbl 1364.60037); \textit{W. König} and the first author, Ann. Inst. Henri Poincaré, Probab. Stat. 53, No. 4, 2214--2228 (2017; Zbl 1382.60107)] to be the limiting object of the mean-field polaron measures, the present identification of the strong coupling limit is a rigorous justification of the mean-field approximation of the polaron problem (on the level of path measures) conjectured by \textit{H. Spohn} in [``Effective mass of the polaron: A functional integral approach'', Ann. Physics 175, 278--318 (1987)]. Replacing the Coulomb potential by continuous function vanishing at infinity and assuming uniqueness (modulo translations) of the relevant variational problem, our proof also shows that path measures coming from a Kac interaction of the above form with translation invariance in space converge to the increments of the corresponding mean-field model.On multiple Schramm-Loewner evolutions.https://www.zbmath.org/1456.602132021-04-16T16:22:00+00:00"Graham, K."https://www.zbmath.org/authors/?q=ai:graham.keith-d|graham.karen-geutherSurface energy and boundary layers for a chain of atoms at low temperature.https://www.zbmath.org/1456.826662021-04-16T16:22:00+00:00"Jansen, Sabine"https://www.zbmath.org/authors/?q=ai:jansen.sabine|jansen.sabine-c"König, Wolfgang"https://www.zbmath.org/authors/?q=ai:konig.wolfgang-d"Schmidt, Bernd"https://www.zbmath.org/authors/?q=ai:schmidt.bernd"Theil, Florian"https://www.zbmath.org/authors/?q=ai:theil.florianSummary: We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed to be small but positive and bounded away from zero, while the temperature \(\beta^{-1}\) goes to zero. Our main results are: (1) As \(\beta \rightarrow \infty\) at fixed positive pressure \(p > 0\), the Gibbs measures \(\mu_\beta\) and \(\nu_\beta\) for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals \(\overline{\mathcal{E}}_\text{bulk}\) and \(\overline{\mathcal{E}}_\text{surf}\). The minimizer of the surface functional corresponds to zero temperature boundary layers; (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of \(\overline{\mathcal{E}}_\text{surf}\); (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts; (4) Bounds on the decay of correlations are provided, some of them uniform in \(\beta\).Flexible two-point selection approach for characteristic function-based parameter estimation of stable laws.https://www.zbmath.org/1456.620342021-04-16T16:22:00+00:00"Kakinaka, Shinji"https://www.zbmath.org/authors/?q=ai:kakinaka.shinji"Umeno, Ken"https://www.zbmath.org/authors/?q=ai:umeno.kenSummary: Stable distribution is one of the attractive models that well describes fat-tail behaviors and scaling phenomena in various scientific fields. The approach based upon the method of moments yields a simple procedure for estimating stable law parameters with the requirement of using momental points for the characteristic function, but the selection of points is only poorly explained and has not been elaborated. We propose a new characteristic function-based approach by introducing a technique of selecting plausible points, which could bring the method of moments available for practical use. Our method outperforms other state-of-art methods that exhibit a closed-form expression of all four parameters of stable laws. Finally, the applicability of the method is illustrated by using several data of financial assets. Numerical results reveal that our approach is advantageous when modeling empirical data with stable distributions.
{\copyright 2020 American Institute of Physics}The Buffon-Laplace needle problem in three dimensions.https://www.zbmath.org/1456.600372021-04-16T16:22:00+00:00"Dell, Zachary E."https://www.zbmath.org/authors/?q=ai:dell.zachary-e"Franklin, Scott V."https://www.zbmath.org/authors/?q=ai:franklin.scott-vSome limit behaviors for the LS estimator in simple linear EV regression models.https://www.zbmath.org/1456.620402021-04-16T16:22:00+00:00"Miao, Yu"https://www.zbmath.org/authors/?q=ai:miao.yu"Wang, Ke"https://www.zbmath.org/authors/?q=ai:wang.ke.2|wang.ke.1|wang.ke.4|wang.ke.3"Zhao, Fangfang"https://www.zbmath.org/authors/?q=ai:zhao.fangfang(no abstract)Power of the MOSUM test for online detection of a transient change in mean.https://www.zbmath.org/1456.601072021-04-16T16:22:00+00:00"Noonan, Jack"https://www.zbmath.org/authors/?q=ai:noonan.jack"Zhigljavsky, Anatoly"https://www.zbmath.org/authors/?q=ai:zhigljavsky.anatoly-aSummary: In this article we discuss an online moving sum (MOSUM) test for detection of a transient change in the mean of a sequence of independent and identically distributed (i.i.d.) normal random variables. By using a well-developed theory for continuous time Gaussian processes and subsequently correcting the results for discrete time, we provide accurate approximations for the average run length (ARL) and power of the test. We check theoretical results against simulations, compare the power of the MOSUM test with that of the cumulative sum (CUSUM), and briefly consider the cases of nonnormal random variables and weighted sums.Local persistence in directed percolation.https://www.zbmath.org/1456.824632021-04-16T16:22:00+00:00"Grassberger, Peter"https://www.zbmath.org/authors/?q=ai:grassberger.peterMoments of continuous-state branching processes with or without immigration.https://www.zbmath.org/1456.602272021-04-16T16:22:00+00:00"Ji, Li-na"https://www.zbmath.org/authors/?q=ai:ji.lina"Li, Zeng-hu"https://www.zbmath.org/authors/?q=ai:li.zenghuLet \(\{X_t; t\ge 0\}\) with \(P(X_0>0)>0\) be a one-dimensional continuous-state branching process in continuous time, \(\{Y_t; t\ge 0\}\) a corresponding process with immigration, and \(f\) a positive continuous function on \([0,\infty)\) satisfying the following condition: There exist constants \(c\ge 0\) and \(K> 0\) such that \(f\) is convex on \([c,\infty)\) and \(f(xy)\le Kf(x)f(y)\) for all \(x,y\in [c,\infty)\). Considering the two processes as solutions of appropriate stochastic integral equations, see \textit{D. A. Dawson} and \textit{Z. Li} [Ann. Probab. 40, No. 2, 813--857 (2012; Zbl 1254.60088)], the authors derive necessary and sufficient conditions, in terms of model parameters, for \(Ef(X_t)<\infty\), \(t>0\), and \(Ef(Y_t)<\infty\), \(t>0\), respectively.
Reviewer: Heinrich Hering (Rockenberg)Positive harmonic functions on groups and covering spaces.https://www.zbmath.org/1456.530532021-04-16T16:22:00+00:00"Polymerakis, Panagiotis"https://www.zbmath.org/authors/?q=ai:polymerakis.panagiotisSummary: We show that if \(p : M \to N\) is a normal Riemannian covering, with \(N\) closed, and \(M\) has exponential volume growth, then there are non-constant, positive harmonic functions on \(M\). This was conjectured by \textit{T. Lyons} and \textit{D. Sullivan} [J. Differ. Geom. 19, 299--323 (1984; Zbl 0554.58022)].A contact process with mobile disorder.https://www.zbmath.org/1456.827302021-04-16T16:22:00+00:00"Dickman, Ronald"https://www.zbmath.org/authors/?q=ai:dickman.ronaldA metric discrepancy result for geometric progression with ratio 3/2.https://www.zbmath.org/1456.111392021-04-16T16:22:00+00:00"Fukuyama, Katusi"https://www.zbmath.org/authors/?q=ai:fukuyama.katusiSummary: We prove the law of the iterated logarithm for discrepancies of the sequence \(\{(3/2)^k x\}\).
For the entire collection see [Zbl 1446.11004].Dynamics of a stochastic tuberculosis transmission model with treatment at home.https://www.zbmath.org/1456.921402021-04-16T16:22:00+00:00"Liu, Qun"https://www.zbmath.org/authors/?q=ai:liu.qun"Jiang, Daqing"https://www.zbmath.org/authors/?q=ai:jiang.daqing"Hayat, Tasawar"https://www.zbmath.org/authors/?q=ai:hayat.tasawar"Alsaedi, Ahmed"https://www.zbmath.org/authors/?q=ai:alsaedi.ahmed"Ahmad, Bashir"https://www.zbmath.org/authors/?q=ai:ahmad.bashir.1|ahmad.bashir.2Summary: In this paper, we consider a stochastic tuberculosis model with two kinds of treatments, that is, treatment at home and treatment in hospital. Firstly, we obtain sufficient conditions for extinction and persistence in the mean of the diseases, then in the case of persistence, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model by constructing a suitable stochastic Lyapunov function. The theoretical results show that large white noise is beneficial for eliminating TB endemic while small white noise is not.SLE local martingales in logarithmic representations.https://www.zbmath.org/1456.602152021-04-16T16:22:00+00:00"Kytölä, Kalle"https://www.zbmath.org/authors/?q=ai:kytola.kalleProbability and statistical inference. 3rd edition.https://www.zbmath.org/1456.620032021-04-16T16:22:00+00:00"Niewiadomska-Bugaj, Magdalena"https://www.zbmath.org/authors/?q=ai:niewiadomska-bugaj.magdalena"Bartoszyński, Robert"https://www.zbmath.org/authors/?q=ai:bartoszynski.robertPublisher's description: Updated classic statistics text, with new problems and examples.
The book helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material.
In this third edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This third edition:
\begin {itemize}
\item Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics
\item ncludes 650 problems and over 400 examples -- an excellent resource for the mathematical statistics class sequence in the increasingly popular ``flipped classroom'' format
\item Offers students in statistics, mathematics, engineering and related fields a user-friendly resource
\item Provides practicing professionals valuable insight into statistical tools
\end {itemize}
The book offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.
See the review of the first edition in [Zbl 0853.62001]. For the second edition see [Zbl 1136.62002].Stochastic functional Hamiltonian system with singular coefficients.https://www.zbmath.org/1456.601472021-04-16T16:22:00+00:00"Huang, Xing"https://www.zbmath.org/authors/?q=ai:huang.xing"Lv, Wujun"https://www.zbmath.org/authors/?q=ai:lv.wujunSummary: By Zvonkin type transforms, the existence and uniqueness of the strong solutions for a class of stochastic functional Hamiltonian systems are obtained, where the drift contains a Hölder-Dini continuous perturbation. Moreover, under some reasonable conditions, the non-explosion of the solution is proved. In addition, as applications, the Harnack and shift Harnack inequalities are derived by method of coupling by change of measure. These inequalities are new even in the case without delay and the shift Harnack inequality is also new even in the non-degenerate functional SDEs with singular drifts.Record statistics for a discrete-time random walk with correlated steps.https://www.zbmath.org/1456.601062021-04-16T16:22:00+00:00"Kearney, Michael J."https://www.zbmath.org/authors/?q=ai:kearney.michael-jExtracting non-Gaussian governing laws from data on mean exit time.https://www.zbmath.org/1456.370932021-04-16T16:22:00+00:00"Zhang, Yanxia"https://www.zbmath.org/authors/?q=ai:zhang.yanxia"Duan, Jinqiao"https://www.zbmath.org/authors/?q=ai:duan.jinqiao"Jin, Yanfei"https://www.zbmath.org/authors/?q=ai:jin.yanfei"Li, Yang"https://www.zbmath.org/authors/?q=ai:li.yang.5Summary: Motivated by the existing difficulties in establishing mathematical models and in observing state time series for some complex systems, especially for those driven by non-Gaussian Lévy motion, we devise a method for extracting non-Gaussian governing laws with observations only on the mean exit time. It is feasible to observe the mean exit time for certain complex systems. With such observations, we use a sparse regression technique in the least squares sense to obtain the approximated function expression of the mean exit time. Then, we learn the generator and further identify the governing stochastic differential equation by solving an inverse problem for a nonlocal partial differential equation and minimizing an error objective function. Finally, we verify the efficacy of the proposed method by three examples with the aid of the simulated data from the original systems. Results show that our method can apply to not only the stochastic dynamical systems driven by Gaussian Brownian motion but also those driven by non-Gaussian Lévy motion, including those systems with complex rational drift.
{\copyright 2020 American Institute of Physics}An extremal problem in uniform distribution theory.https://www.zbmath.org/1456.111332021-04-16T16:22:00+00:00"Baláž, Vladimír"https://www.zbmath.org/authors/?q=ai:balaz.vladimir"Iacò, Maria Rita"https://www.zbmath.org/authors/?q=ai:iaco.maria-rita"Strauch, Oto"https://www.zbmath.org/authors/?q=ai:strauch.oto"Thonhauser, Stefan"https://www.zbmath.org/authors/?q=ai:thonhauser.stefan"Tichy, Robert F."https://www.zbmath.org/authors/?q=ai:tichy.robert-franzLet $x_n$ and $y_n$, $n= 1,2,\dots$ be uniformly distributed sequences in the unit interval and $F$ be a given continuous function on $[0,1]^2$. A classical problem is the study of extremal limits of the form $\frac1N\sum_{n=1}^NF(x_n, y_n)$, where $N\to\infty$. It is equivalent to find optimal bounds for Riemann-Stieltjes integrals of the form $\int_0^1\int_0^1 F(x, y)dC(x, y)$, where $C$ is the asymptotic distribution function of the sequence $(x_n, y_n)$ and it is usually referred to as copula. As pointed out in [the reviewer and \textit{O. Strauch}, Unif. Distrib. Theory 6, No. 1, 101--125 (2011; Zbl 1313.11089)] the solution of this problem depends on the sign of the partial derivative $\frac{\partial^2F(x,y)}{\partial x\partial y}$.
The main result of the paper is the following: Let $0< x_1< x_2<1$ and
\[
F(x, y) =\begin{cases}
F_1(x, y) &\text{if }x\in (0, x_1),\frac{\partial^2F_1(x,y)}{\partial x\partial y}>0,\\
F_2(x, y) &\text{if }x\in (x_1, x_2),\frac{\partial^2F_2(x,y)}{\partial x\partial y}<0,\\
F_3(x, y) &\text{if }x\in (x_2,1),\frac{\partial^2F_3(x,y)}{\partial x\partial y}>0.\end{cases}
\]
Then the copula maximizing $\int_0^1\int_0^1 F(x, y)d\tilde{C}(x, y)$ has the form
\[
C(x, y) =\begin{cases}
\min(x, h_1(y))&\text{if }x\in [0, x_1],\\
\max(x+h_2(y)-x_2, h_1(y)) &\text{if }x\in [x_1, x_2],\\
\min(x-x_2+h_2(y), y)&\text{if }x\in [x_2,1],\end{cases}
\]
where $h_1(y) =C(x_1, y)$, $h_2(y) =C(x_2, y)$ and $(h_1, h_2)$ satisfy the Euler-Lagrange differential equations. The authors also discuss connections of extremal limits of couples to the theory of optimal transport. In the final section, they solve the example $F(x, y) = \sin(\pi(x+y))$ and relate this problem to combinatorial optimization based on the work of \textit{L. Uckelmann} [in: Distributions with given marginals and moment problems. Proceedings of the 1996 conference, Prague, Czech Republic. Dordrecht: Kluwer Academic Publishers. 275--281 (1997; Zbl 0907.60022)].
Reviewer: Jana Fialová (Trnava)A Lagrangian scheme for numerical evaluation of the noncausal stochastic integral.https://www.zbmath.org/1456.601352021-04-16T16:22:00+00:00"Ogawa, Shigeyoshi"https://www.zbmath.org/authors/?q=ai:ogawa.shigeyoshiSummary: We are concerned with a noncausal approach to the numerical evaluation of the stochastic integral \(\int f dW_t\) with respect to Brownian motion. Viewed as a special case of the numerical solution (in strong sense) of the SDE, it may be believed that the precision level of such an approximation scheme that uses only a finite number of increments \(\Delta_kW=W(t_{k+1})-W(t_k)\) of Brownian motion, would not exceed the order \(O\big (\frac{1}{n}\big )\) where \(n\) is the number of steps for discretization. We present in this note a simple but not trivial example showing that this belief is not correct. The discussion is developed on the basis of the noncausal theory of stochastic calculus introduced by the author.Off-critical SLE(2) and SLE(4): a field theory approach.https://www.zbmath.org/1456.824292021-04-16T16:22:00+00:00"Bauer, Michel"https://www.zbmath.org/authors/?q=ai:bauer.michel"Bernard, Denis"https://www.zbmath.org/authors/?q=ai:bernard.denis"Cantini, Luigi"https://www.zbmath.org/authors/?q=ai:cantini.luigiImprovement of random coefficient differential models of growth of anaerobic photosynthetic bacteria by combining Bayesian inference and gPC.https://www.zbmath.org/1456.340462021-04-16T16:22:00+00:00"Calatayud, Julia"https://www.zbmath.org/authors/?q=ai:calatayud.julia"Cortés, Juan Carlos"https://www.zbmath.org/authors/?q=ai:cortes.juan-carlos"Jornet, Marc"https://www.zbmath.org/authors/?q=ai:jornet.marcSummary: The time evolution of microorganisms, such as bacteria, is of great interest in biology. In the article by \textit{D. Stanescu} et al. [ETNA, Electron. Trans. Numer. Anal. 34, 44--58 (2009; Zbl 1173.60333)], a logistic model was proposed to model the growth of anaerobic photosynthetic bacteria. In the laboratory experiment, actual data for two species of bacteria were considered: \textit{Rhodobacter capsulatus} and \textit{Chlorobium vibrioforme}. In this paper, we suggest a new nonlinear model by assuming that the population growth rate is not proportional to the size of the bacteria population, but to the number of interactions between the microorganisms, and by taking into account the beginning of the death phase in the kinetic curve. Stanescu et al. evaluated the effect of randomness into the model coefficients by using generalized polynomial chaos (gPC) expansions, by setting arbitrary distributions without taking into account the likelihood of the data. By contrast, we utilize a Bayesian inverse approach for parameter estimation to obtain reliable posterior distributions for the random input coefficients in both the logistic and our new model. Since our new model does not possess an explicit solution, we use gPC expansions to construct the Bayesian model and to accelerate the Markov chain Monte Carlo algorithm for the Bayesian inference.Theta functions and Brownian motion.https://www.zbmath.org/1456.580252021-04-16T16:22:00+00:00"Duncan, Tyrone E."https://www.zbmath.org/authors/?q=ai:duncan.tyrone-eSummary: A theta function for an arbitrary connected and simply connected compact simple Lie group is defined as an infinite determinant that is naturally related to the transformation of a family of independent Gaussian random variables associated with a pinned Brownian motion in the Lie group. From this definition of a theta function, the equality of the product and the sum expressions for a theta function is obtained. This equality for an arbitrary connected and simply connected compact simple Lie group is known as a Macdonald identity which generalizes the Jacobi triple product for the elliptic theta function associated with \textit{su}(2).Angles of the Gaussian simplex.https://www.zbmath.org/1456.600432021-04-16T16:22:00+00:00"Kabluchko, Z."https://www.zbmath.org/authors/?q=ai:kabluchko.zakhar-a"Zaporozhets, D."https://www.zbmath.org/authors/?q=ai:zaporozhets.dmitrySummary: Consider a \(d\)-dimensional simplex whose vertices are random points chosen independently according to the standard Gaussian distribution on \(\mathbb{R}^d\). We prove that the expected angle sum of this random simplex equals the angle sum of the regular simplex of the same dimension \(d\).Distribution of extreme first passage times of diffusion.https://www.zbmath.org/1456.920072021-04-16T16:22:00+00:00"Lawley, Sean D."https://www.zbmath.org/authors/?q=ai:lawley.sean-dSummary: Many events in biology are triggered when a diffusing searcher finds a target, which is called a first passage time (FPT). The overwhelming majority of FPT studies have analyzed the time it takes a single searcher to find a target. However, the more relevant timescale in many biological systems is the time it takes the fastest searcher(s) out of many searchers to find a target, which is called an extreme FPT. In this paper, we apply extreme value theory to find a tractable approximation for the full probability distribution of extreme FPTs of diffusion. This approximation can be easily applied in many diverse scenarios, as it depends on only a few properties of the short time behavior of the survival probability of a single FPT. We find this distribution by proving that a careful rescaling of extreme FPTs converges in distribution as the number of searchers grows. This limiting distribution is a type of Gumbel distribution and involves the LambertW function. This analysis yields new explicit formulas for approximations of statistics of extreme FPTs (mean, variance, moments, etc.) which are highly accurate and are accompanied by rigorous error estimates.Nonequilibrium stationary states with Gibbs measure for two or three species of interacting particles.https://www.zbmath.org/1456.826772021-04-16T16:22:00+00:00"Luck, J. M."https://www.zbmath.org/authors/?q=ai:luck.jean-marc"Godrèche, C."https://www.zbmath.org/authors/?q=ai:godreche.claudeThe ensemble of random Markov matrices.https://www.zbmath.org/1456.825042021-04-16T16:22:00+00:00"Horvat, Martin"https://www.zbmath.org/authors/?q=ai:horvat.martinPolynomial copula transformations.https://www.zbmath.org/1456.620972021-04-16T16:22:00+00:00"Tasena, Santi"https://www.zbmath.org/authors/?q=ai:tasena.santiSummary: In this study, we demonstrate that the problem of characterizing polynomial copula transformations can be reduced to solving a system of (in)equalities. In this case, no knowledge of copulas is necessary to find an instance of such polynomials, or even the whole set of such polynomials. As a demonstration, we employ this result to characterize all quadratic polynomials that define copula transformations.A robust unscented transformation for uncertain moments.https://www.zbmath.org/1456.651802021-04-16T16:22:00+00:00"Kussaba, Hugo T. M."https://www.zbmath.org/authors/?q=ai:kussaba.hugo-tadashi-m"Ishihara, João Y."https://www.zbmath.org/authors/?q=ai:ishihara.joao-yoshiyuki"Menezes, Leonardo R. A. X."https://www.zbmath.org/authors/?q=ai:menezes.leonardo-r-a-xIn numerous problems of statistics and stochastic filtering, one is often interested in calculating the posterior expectation of a continuous random variable that undergoes a nonlinear transform.
The authors propose a robust version of the unscented transform (UT) for one-dimensional random variables. The principle behind UT is to approximate the continuous distribution by the discrete distribution by equating the first \(m\) moments of these distributions. UT is a deterministic sampling technique and has less computational burden than the Monte Carlo integration method.
In the paper, it is proposed to use the Chebyshev center of the semialgebraic set defined by the possible choices of sigma points and their weights as a robust UT. As the moments are not usually exactly known in practical situations, it is assumed that they lie in some intervals.
Two approaches for generating robust sigma points are proposed. The moment matching equations of UT are reformulated as a system of polynomial equations with polynomial inequalities. As this system can have more than one solution, it is possible to choose a set of sigma points which minimizes a given cost function by formulating the problem as a polynomial optimization problem solved by using Lasserre's hierarchy of semidefinite programming relaxations.
The main contribution of the paper is the introduction of the concept of UT robustness in the sense of exploiting the upper and lower bounds for moments. Robustness is achieved by matching precisely known high order moments. Lasserre's hierarchy of relaxations is applied to polynomial equations with polynomial inequalities.
Reviewer: Ctirad Matonoha (Praha)Shaping large Poisson Voronoi cells in two dimensions.https://www.zbmath.org/1456.600392021-04-16T16:22:00+00:00"Gabrielli, Andrea"https://www.zbmath.org/authors/?q=ai:gabrielli.andrea(no abstract)Non-classical large deviations for a noisy system with non-isolated attractors.https://www.zbmath.org/1456.825462021-04-16T16:22:00+00:00"Bouchet, Freddy"https://www.zbmath.org/authors/?q=ai:bouchet.freddy"Touchette, Hugo"https://www.zbmath.org/authors/?q=ai:touchette.hugoExact matrix-product states for parallel dynamics: open boundaries and excess mass on the ring.https://www.zbmath.org/1456.826332021-04-16T16:22:00+00:00"Woelki, Marko"https://www.zbmath.org/authors/?q=ai:wolki.marko"Schreckenberg, Michael"https://www.zbmath.org/authors/?q=ai:schreckenberg.michaelAlignment percolation.https://www.zbmath.org/1456.602492021-04-16T16:22:00+00:00"Beaton, Nicholas R."https://www.zbmath.org/authors/?q=ai:beaton.nicholas-r"Grimmett, Geoffrey R."https://www.zbmath.org/authors/?q=ai:grimmett.geoffrey-r"Holmes, Mark"https://www.zbmath.org/authors/?q=ai:holmes.mark-h|holmes.mark-d|holmes.mark-p|holmes.mark-jSummary: The existence (or not) of infinite clusters is explored for two stochastic models of intersecting line segments in \(d \geqslant 2\) dimensions. Salient features of the phase diagram are established in each case. The models are based on site percolation on \(\mathbb{Z}^d\) with parameter \(p\in (0,1]\). For each occupied site \(v\), and for each of the \(2d\) possible coordinate directions, declare the entire line segment from \(v\) to the next occupied site in the given direction to be either blue or not blue according to a given stochastic rule. In the `one-choice model', each occupied site declares one of its \(2d\) incident segments to be blue. In the `independent model', the states of different line segments are independent.Large deviation inequalities of LS estimator in nonlinear regression models.https://www.zbmath.org/1456.620462021-04-16T16:22:00+00:00"Miao, Yu"https://www.zbmath.org/authors/?q=ai:miao.yu"Tang, Yanyan"https://www.zbmath.org/authors/?q=ai:tang.yanyanSummary: In the paper, the large deviation inequalities of the LS estimator for the nonlinear regression model with martingale differences errors are established. The assumptions for the errors are (conditional) exponential integrability which weaken the bounded condition in [\textit{H. Shuhe}, Stochastic Processes Appl. 47, No. 2, 345--352 (1993; Zbl 0786.62066)]. As an application, we give the large deviation inequalities of LS estimator for the simple Michaelis-Menten model.On the study of forward Kolmogorov system and the corresponding problems for inhomogeneous continuous-time Markov chains.https://www.zbmath.org/1456.601912021-04-16T16:22:00+00:00"Zeifman, Alexander"https://www.zbmath.org/authors/?q=ai:zeifman.alexander-iSummary: An inhomogeneous continuous-time Markov chain X(t) with finite or countable state space under some natural additional assumptions is considered. As a consequence, we study a number of problems for the corresponding forward Kolmogorov system, which is the linear system of differential equations with special structure of the matrix A(t). In the countable situation we have an equation in the space of sequences \(l_1\). The important properties of X(t) (such as weak and strong ergodicity, perturbation bounds, truncation bounds) are closely connected with behaviour of the solutions of the forward Kolmogorov system as \(t \rightarrow \infty \). The main problems and some approaches for their solution are discussed in the paper.
For the entire collection see [Zbl 1445.34003].Control of noise in gene expression by transcriptional reinitiation.https://www.zbmath.org/1456.920562021-04-16T16:22:00+00:00"Karmakar, Rajesh"https://www.zbmath.org/authors/?q=ai:karmakar.rajeshArithmetic area for \(m\) planar Brownian paths.https://www.zbmath.org/1456.602082021-04-16T16:22:00+00:00"Desbois, Jean"https://www.zbmath.org/authors/?q=ai:desbois.jean"Ouvry, Stéphane"https://www.zbmath.org/authors/?q=ai:ouvry.stephaneProperties of sparse random matrices over finite fields.https://www.zbmath.org/1456.824822021-04-16T16:22:00+00:00"Alamino, Roberto C."https://www.zbmath.org/authors/?q=ai:alamino.roberto-c"Saad, David"https://www.zbmath.org/authors/?q=ai:saad.davidGenerally covariant \(N\)-particle dynamics.https://www.zbmath.org/1456.530542021-04-16T16:22:00+00:00"Miller, Tomasz"https://www.zbmath.org/authors/?q=ai:miller.tomasz"Eckstein, Michał"https://www.zbmath.org/authors/?q=ai:eckstein.michal"Horodecki, Paweł"https://www.zbmath.org/authors/?q=ai:horodecki.pawel"Horodecki, Ryszard"https://www.zbmath.org/authors/?q=ai:horodecki.ryszardSummary: A simultaneous description of the dynamics of multiple particles requires a configuration space approach with an external time parameter. This is in stark contrast with the relativistic paradigm, where time is but a coordinate chosen by an observer. Here we show, however, that the two attitudes towards modelling \(N\)-particle dynamics can be conciliated within a generally covariant framework. To this end we construct an `\(N\)-particle configuration spacetime' \(\mathcal{M}_{(N)} \), starting from a globally hyperbolic spacetime \(\mathcal{M}\) with a chosen smooth splitting into time and space components. The dynamics of multi-particle systems is modelled at the level of Borel probability measures over \(\mathcal{M}_{(N)}\) with the help of the global time parameter. We prove that with any time-evolution of measures, which respects the \(N\)-particle causal structure of \(\mathcal{M}_{(N)}\), one can associate a single measure on the Polish space of `\(N\)-particle wordlines'. The latter is a splitting-independent object, from which one can extract the evolution of measures for any other global observer on \(\mathcal{M}\). An additional asset of the adopted measure-theoretic framework is the possibility to model the dynamics of indistinguishable entities, such as quantum particles. As an application we show that the multi-photon and multi-fermion Schrödinger equations, although explicitly dependent on the choice of an external time-parameter, are in fact fully compatible with the causal structure of the Minkowski spacetime.On the duration and intensity of cumulative advantage competitions.https://www.zbmath.org/1456.601832021-04-16T16:22:00+00:00"Jiang, Bo"https://www.zbmath.org/authors/?q=ai:jiang.bo"Sun, Liyuan"https://www.zbmath.org/authors/?q=ai:sun.liyuan"Figueiredo, Daniel R."https://www.zbmath.org/authors/?q=ai:figueiredo.daniel-ratton"Ribeiro, Bruno"https://www.zbmath.org/authors/?q=ai:ribeiro.bruno-v|ribeiro.bruno-f-m"Towsley, Don"https://www.zbmath.org/authors/?q=ai:towsley.donSimple matrix models for random Bergman metrics.https://www.zbmath.org/1456.824992021-04-16T16:22:00+00:00"Ferrari, Frank"https://www.zbmath.org/authors/?q=ai:ferrari.frank"Klevtsov, Semyon"https://www.zbmath.org/authors/?q=ai:klevtsov.semyon"Zelditch, Steve"https://www.zbmath.org/authors/?q=ai:zelditch.steveAlgebraic Bethe ansatz approach to the asymptotic behavior of correlation functions.https://www.zbmath.org/1456.822782021-04-16T16:22:00+00:00"Kitanine, N."https://www.zbmath.org/authors/?q=ai:kitanine.n-a"Kozlowski, K. K."https://www.zbmath.org/authors/?q=ai:kozlowski.karol-kajetan"Maillet, J. M."https://www.zbmath.org/authors/?q=ai:maillet.jean-michel"Slavnov, N. A."https://www.zbmath.org/authors/?q=ai:slavnov.nikita-a"Terras, V."https://www.zbmath.org/authors/?q=ai:terras.veroniqueExpected dispersion of uniformly distributed points.https://www.zbmath.org/1456.600422021-04-16T16:22:00+00:00"Hinrichs, Aicke"https://www.zbmath.org/authors/?q=ai:hinrichs.aicke"Krieg, David"https://www.zbmath.org/authors/?q=ai:krieg.david"Kunsch, Robert J."https://www.zbmath.org/authors/?q=ai:kunsch.robert-j"Rudolf, Daniel"https://www.zbmath.org/authors/?q=ai:rudolf.danielSummary: The dispersion of a point set in \([0,1]^d\) is the volume of the largest axis parallel box inside the unit cube that does not intersect the point set. We study the expected dispersion with respect to a random set of \(n\) points determined by an i.i.d. sequence of uniformly distributed random variables. Depending on the number of points \(n\) and the dimension \(d\) we provide an upper and a lower bound of the expected dispersion. In particular, we show that the minimal number of points required to achieve an expected dispersion less than \(\varepsilon\in(0,1)\) depends linearly on the dimension \(d\).Critical behavior of the geometrical spin clusters and interfaces in the two-dimensional thermalized bond Ising model.https://www.zbmath.org/1456.823922021-04-16T16:22:00+00:00"Davatolhagh, S."https://www.zbmath.org/authors/?q=ai:davatolhagh.s"Moshfeghian, M."https://www.zbmath.org/authors/?q=ai:moshfeghian.m"Saberi, A. A."https://www.zbmath.org/authors/?q=ai:saberi.abbas-aliKingman's coalescent with erosion.https://www.zbmath.org/1456.602312021-04-16T16:22:00+00:00"Foutel-Rodier, Félix"https://www.zbmath.org/authors/?q=ai:foutel-rodier.felix"Lambert, Amaury"https://www.zbmath.org/authors/?q=ai:lambert.amaury"Schertzer, Emmanuel"https://www.zbmath.org/authors/?q=ai:schertzer.emmanuelSummary: Consider the Markov process taking values in the partitions of \(\mathbb{N}\) such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate \(d\). This is a special case of exchangeable fragmentation-coalescence process, called Kingman's coalescent with erosion. We provide a new construction of the stationary distribution of this process as a sample from a standard flow of bridges. This allows us to give a representation of the asymptotic frequencies of this stationary distribution in terms of a sequence of independent diffusions. Moreover, we introduce a new process valued in the partitions of \(\mathbb{Z}\) called Kingman's coalescent with immigration, where pairs of blocks coalesce at rate one, and new blocks of size one immigrate according to a Poisson process of intensity \(d\). By coupling Kingman's coalescents with erosion and with immigration, we are able to show that the size of a block chosen uniformly at random from the stationary distribution of the restriction of Kingman's coalescent with erosion to \(\{1,\dots,n\}\) converges as \(n\to\infty\) to the total progeny of a critical binary branching process.Approximation of the first passage time distribution for the birth-death processes.https://www.zbmath.org/1456.601902021-04-16T16:22:00+00:00"Kononovicius, Aleksejus"https://www.zbmath.org/authors/?q=ai:kononovicius.aleksejus"Gontis, Vygintas"https://www.zbmath.org/authors/?q=ai:gontis.vygintasIndifferentiability of truncated random permutations.https://www.zbmath.org/1456.940652021-04-16T16:22:00+00:00"Choi, Wonseok"https://www.zbmath.org/authors/?q=ai:choi.wonseok"Lee, Byeonghak"https://www.zbmath.org/authors/?q=ai:lee.byeonghak"Lee, Jooyoung"https://www.zbmath.org/authors/?q=ai:lee.jooyoungSummary: One of natural ways of constructing a pseudorandom function from a pseudorandom permutation is to simply truncate the output of the permutation. When \(n\) is the permutation size and \(m\) is the number of truncated bits, the resulting construction is known to be indistinguishable from a random function up to \(2^{\frac{n+m}{2}}\) queries, which is tight.
In this paper, we study the indifferentiability of a truncated random permutation where a fixed prefix is prepended to the inputs. We prove that this construction is (regularly) indifferentiable from a public random function up to \(\mathrm{min}\{2^{\frac{n+m}{3}},2^m, 2^\ell \}\) queries, while it is publicly indifferentiable up to \(\mathrm{min}\{\mathrm{max}\{2^{\frac{n+m}{3}},2^{\frac{n}{2}}\},2^\ell\}\) queries, where \(\ell\) is the size of the fixed prefix. Furthermore, the regular indifferentiability bound is proved to be tight when \(m+\ell\ll n\).
Our results significantly improve upon the previous bound of \(\min\{ 2^{\frac{m}{2}},2^\ell\}\) given by \textit{Y. Dodis} et al. [Lect. Notes Comput. Sci. 5665, 104--121 (2009; Zbl 1248.94065)], allowing us to construct, for instance, an \(\frac{n}{2}\)-to-\(\frac{n}{2}\) bit random function that makes a single call to an \(n\)-bit permutation, achieving \(\frac{n}{2}\)-bit security.
For the entire collection see [Zbl 1428.94008].A new approach to interval-valued probability measures, a formal method for consolidating the languages of information deficiency: foundations.https://www.zbmath.org/1456.600102021-04-16T16:22:00+00:00"Jamison, K. David"https://www.zbmath.org/authors/?q=ai:jamison.k-david"Lodwick, Weldon A."https://www.zbmath.org/authors/?q=ai:lodwick.weldon-alexanderSummary: This article proposes a new formal definition of an interval valued probability measure (IVPM) based on a measure theoretic foundation, and shows that various uncertainties that occur in data associated in mathematical analyses, for example, in optimization under uncertainty models, can be unified and formulated within this one common IVPM framework facilitating the solution of many mathematical problems. This article develops a theory, we call generalized uncertainty theory, that will be characterized by the generation of upper and lower bounding functions enclosing all distributions that are possible from the given partial information.Condensation for random variables conditioned by the value of their sum.https://www.zbmath.org/1456.601042021-04-16T16:22:00+00:00"Godrèche, Claude"https://www.zbmath.org/authors/?q=ai:godreche.claudeUnbiased truncated quadratic variation for volatility estimation in jump diffusion processes.https://www.zbmath.org/1456.620382021-04-16T16:22:00+00:00"Amorino, Chiara"https://www.zbmath.org/authors/?q=ai:amorino.chiara"Gloter, Arnaud"https://www.zbmath.org/authors/?q=ai:gloter.arnaudSummary: The problem of integrated volatility estimation for an Ito semimartingale is considered under discrete high-frequency observations in short time horizon. We provide an asymptotic expansion for the integrated volatility that gives us, in detail, the contribution deriving from the jump part. The knowledge of such a contribution allows us to build an unbiased version of the truncated quadratic variation, in which the bias is visibly reduced. In earlier results to have the original truncated realized volatility well-performed the condition \(\beta>\frac{1}{2(2-\alpha)}\) on \(\beta\) (that is such that \((\frac{1}{n})^\beta\) is the threshold of the truncated quadratic variation) and on the degree of jump activity \(\alpha\) was needed (see [\textit{C. Mancini}, ibid. 121, No. 4, 845--855 (2011; Zbl 1216.62159); \textit{J. Jacod}, ibid. 118, No. 4, 517--559 (2008; Zbl 1142.60022)]). In this paper we theoretically relax this condition and we show that our unbiased estimator achieves excellent numerical results for any couple \((\alpha,\beta)\).Generalized transforms and generalized convolution products associated with Gaussian paths on function space.https://www.zbmath.org/1456.600832021-04-16T16:22:00+00:00"Chang, Seung Jun"https://www.zbmath.org/authors/?q=ai:chang.seung-jun"Choi, Jae Gil"https://www.zbmath.org/authors/?q=ai:choi.jae-gilSummary: In this paper we define a more general convolution product (associated with Gaussian processes) of functionals on the function space \(C_{a,b}[0,T]\). The function space \(C_{a,b}[0,T]\) is induced by a generalized Brownian motion process. Thus the Gaussian processes used in this paper are non-centered processes. We then develop the fundamental relationships between the generalized Fourier-Feynman transform associated with the Gaussian process and the convolution product.Propagation of chaos for topological interactions.https://www.zbmath.org/1456.602542021-04-16T16:22:00+00:00"Degond, P."https://www.zbmath.org/authors/?q=ai:degond.pierre"Pulvirenti, M."https://www.zbmath.org/authors/?q=ai:pulvirenti.marioSummary: We consider a \(N\)-particle model describing an alignment mechanism due to a topological interaction among the agents. We show that the kinetic equation, expected to hold in the mean-field limit \(N\rightarrow \infty \), as following from the previous analysis in [\textit{A. Blanchet} and \textit{P. Degond}, J. Stat. Phys. 163, No. 1, 41--60 (2016; Zbl 1352.92182)] can be rigorously derived. This means that the statistical independence (propagation of chaos) is indeed recovered in the limit, provided it is assumed at time zero.Correlation function for the grid-Poisson Euclidean matching on a line and on a circle.https://www.zbmath.org/1456.910642021-04-16T16:22:00+00:00"Boniolo, Elena"https://www.zbmath.org/authors/?q=ai:boniolo.elena"Caracciolo, Sergio"https://www.zbmath.org/authors/?q=ai:caracciolo.sergio"Sportiello, Andrea"https://www.zbmath.org/authors/?q=ai:sportiello.andreaA Berry-Esseén theorem for partial sums of functionals of heavy-tailed moving averages.https://www.zbmath.org/1456.600512021-04-16T16:22:00+00:00"Basse-O'Connor, Andreas"https://www.zbmath.org/authors/?q=ai:basse-oconnor.andreas"Podolskij, Mark"https://www.zbmath.org/authors/?q=ai:podolskij.mark"Thäle, Christoph"https://www.zbmath.org/authors/?q=ai:thale.christophSummary: In this paper we obtain Berry-Esseén bounds on partial sums of functionals of heavy-tailed moving averages, including the linear fractional stable noise, stable fractional ARIMA processes and stable Ornstein-Uhlenbeck processes. Our rates are obtained for the Wasserstein and Kolmogorov distances, and depend strongly on the interplay between the memory of the process, which is controlled by a parameter \(\alpha\), and its tail-index, which is controlled by a parameter \(\beta\). In fact, we obtain the classical \(1/\sqrt{n}\) rate of convergence when the tails are not too heavy and the memory is not too strong, more precisely, when \(\alpha\beta>3\) or \(\alpha\beta>4\) in the case of Wasserstein and Kolmogorov distance, respectively.
Our quantitative bounds rely on a new second-order Poincaré inequality on the Poisson space, which we derive through a combination of Stein's method and Malliavin calculus. This inequality improves and generalizes a result by \textit{G. Last} et al. [Probab. Theory Relat. Fields 165, No. 3--4, 667--723 (2016; Zbl 1347.60012)].Joint probability distributions and fluctuation theorems.https://www.zbmath.org/1456.825542021-04-16T16:22:00+00:00"García-García, Reinaldo"https://www.zbmath.org/authors/?q=ai:garcia-garcia.reinaldo"Lecomte, Vivien"https://www.zbmath.org/authors/?q=ai:lecomte.vivien"Kolton, Alejandro B."https://www.zbmath.org/authors/?q=ai:kolton.alejandro-b"Domínguez, Daniel"https://www.zbmath.org/authors/?q=ai:dominguez.danielCoupled nonlinear stochastic differential equations generating arbitrary distributed observable with \(1/f\) noise.https://www.zbmath.org/1456.601522021-04-16T16:22:00+00:00"Ruseckas, J."https://www.zbmath.org/authors/?q=ai:ruseckas.julius"Kazakevičius, R."https://www.zbmath.org/authors/?q=ai:kazakevicius.rytis"Kaulakys, B."https://www.zbmath.org/authors/?q=ai:kaulakys.bDirected, cylindric and radial Brownian webs.https://www.zbmath.org/1456.602062021-04-16T16:22:00+00:00"Coupier, David"https://www.zbmath.org/authors/?q=ai:coupier.david"Marckert, Jean-François"https://www.zbmath.org/authors/?q=ai:marckert.jean-francois"Tran, Viet Chi"https://www.zbmath.org/authors/?q=ai:tran.viet-chiSummary: The Brownian web (BW) is a collection of coalescing Brownian paths \((W_{(x,t)},(x,t) \in \mathbb{R} ^2)\) indexed by the plane. It appears in particular as continuous limit of various discrete models of directed forests of coalescing random walks and navigation schemes. Radial counterparts have been considered but global invariance principles are hard to establish. In this paper, we consider cylindrical forests which in some sense interpolate between the directed and radial forests: we keep the topology of the plane while still taking into account the angular component. We define in this way the cylindric Brownian web (CBW), which is locally similar to the planar BW but has several important macroscopic differences. For example, in the CBW, the coalescence time between two paths admits exponential moments and the CBW as its dual contain each a.s. a unique bi-infinite path. This pair of bi-infinite paths is distributed as a pair of reflected Brownian motions on the cylinder. Projecting the CBW on the radial plane, we obtain a radial Brownian web (RBW), i.e. a family of coalescing paths where under a natural parametrization, the angular coordinate of a trajectory is a Brownian motion. Recasting some of the discrete radial forests of the literature on the cylinder, we propose rescalings of these forests that converge to the CBW, and deduce the global convergence of the corresponding rescaled radial forests to the RBW. In particular, a modification of the radial model proposed in \textit{C.F. Coletti} and \textit{L.A. Valencia} [``Scaling limit for a family of random paths with radial behavior'', Preprint, \url{arXiv:1310.6929}] is shown to converge to the CBW.Generalized stochastic resonance in a linear fractional system with a random delay.https://www.zbmath.org/1456.827672021-04-16T16:22:00+00:00"Gao, Shi-Long"https://www.zbmath.org/authors/?q=ai:gao.shilongOn multidimensional record patterns.https://www.zbmath.org/1456.601262021-04-16T16:22:00+00:00"Krapivsky, P. L."https://www.zbmath.org/authors/?q=ai:krapivsky.pavel-l"Luck, J. M."https://www.zbmath.org/authors/?q=ai:luck.jean-marcDynamical properties of a stochastic predator-prey model with functional response.https://www.zbmath.org/1456.921232021-04-16T16:22:00+00:00"Lv, Jingliang"https://www.zbmath.org/authors/?q=ai:lv.jingliang"Zou, Xiaoling"https://www.zbmath.org/authors/?q=ai:zou.xiaoling"Li, Yujie"https://www.zbmath.org/authors/?q=ai:li.yujieSummary: A stochastic prey-predator model with functional response is investigated in this paper. A complete threshold analysis of coexistence and extinction is obtained. Moreover, we point out that the stochastic predator-prey model undergoes a stochastic Hopf bifurcation from the viewpoint of numerical simulations. Some numerical simulations are carried out to support our results.Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes.https://www.zbmath.org/1456.827692021-04-16T16:22:00+00:00"González Arenas, Zochil"https://www.zbmath.org/authors/?q=ai:arenas.zochil-gonzalez"Barci, Daniel G."https://www.zbmath.org/authors/?q=ai:barci.daniel-gHigh excursions of Gaussian nonstationary processes in discrete time.https://www.zbmath.org/1456.600862021-04-16T16:22:00+00:00"Kozik, I. A."https://www.zbmath.org/authors/?q=ai:kozik.i-a"Piterbarg, V. I."https://www.zbmath.org/authors/?q=ai:piterbarg.vladimir-iSummary: Exact asymptotic behavior is given for high excursion probabilities of Gaussian processes in discrete time as the corresponding lattice pitch unboundedly decreases. The proximity of the asymptotic behavior to that in continuous time is discussed. Examples are given related to fractional Brownian motion and the corresponding ruin problem.Nonlocal stationary probability distributions and escape rates for an active Ornstein-Uhlenbeck particle.https://www.zbmath.org/1456.602212021-04-16T16:22:00+00:00"Woillez, Eric"https://www.zbmath.org/authors/?q=ai:woillez.eric"Kafri, Yariv"https://www.zbmath.org/authors/?q=ai:kafri.yariv"Lecomte, Vivien"https://www.zbmath.org/authors/?q=ai:lecomte.vivienThe large deviation function for entropy production: the optimal trajectory and the role of fluctuations.https://www.zbmath.org/1456.602752021-04-16T16:22:00+00:00"Speck, Thomas"https://www.zbmath.org/authors/?q=ai:speck.thomas"Engel, Andreas"https://www.zbmath.org/authors/?q=ai:engel.andreas|engel.andreas-k"Seifert, Udo"https://www.zbmath.org/authors/?q=ai:seifert.udoEntropy production of nonequilibrium steady states with irreversible transitions.https://www.zbmath.org/1456.370122021-04-16T16:22:00+00:00"Zeraati, Somayeh"https://www.zbmath.org/authors/?q=ai:zeraati.somayeh"Jafarpour, Farhad H."https://www.zbmath.org/authors/?q=ai:jafarpour.farhad-h"Hinrichsen, Haye"https://www.zbmath.org/authors/?q=ai:hinrichsen.hayeInteraction quench in a trapped 1D Bose gas.https://www.zbmath.org/1456.811132021-04-16T16:22:00+00:00"Mazza, Paolo P."https://www.zbmath.org/authors/?q=ai:mazza.paolo-p"Collura, Mario"https://www.zbmath.org/authors/?q=ai:collura.mario"Kormos, Márton"https://www.zbmath.org/authors/?q=ai:kormos.marton"Calabrese, Pasquale"https://www.zbmath.org/authors/?q=ai:calabrese.pasqualeConfluence of geodesic paths and separating loops in large planar quadrangulations.https://www.zbmath.org/1456.822312021-04-16T16:22:00+00:00"Bouttier, J."https://www.zbmath.org/authors/?q=ai:bouttier.jeremie"Guitter, E."https://www.zbmath.org/authors/?q=ai:guitter.emmanuelAsymptotic theory for near integrated processes driven by tempered linear processes.https://www.zbmath.org/1456.622152021-04-16T16:22:00+00:00"Sabzikar, Farzad"https://www.zbmath.org/authors/?q=ai:sabzikar.farzad"Wang, Qiying"https://www.zbmath.org/authors/?q=ai:wang.qiying"Phillips, Peter C. B."https://www.zbmath.org/authors/?q=ai:phillips.peter-c-bSummary: In an early article on near-unit root autoregression, \textit{J. Ahtola} and \textit{G. C. Tiao} [``Parameter inference for a nearly nonstationary first order autoregressive model'', Biometrika 71, No. 2, 263--272 (1984; \url{doi:10.1093/biomet/71.2.263})] studied the behavior of the score function in a stationary first order autoregression driven by independent Gaussian innovations as the autoregressive coefficient approached unity from below. The present paper develops asymptotic theory for near-integrated random processes and associated regressions including the score function in more general settings where the errors are tempered linear processes. Tempered processes are stationary time series that have a semi-long memory property in the sense that the autocovariogram of the process resembles that of a long memory model for moderate lags but eventually diminishes exponentially fast according to the presence of a decay factor governed by a tempering parameter. When the tempering parameter is sample size dependent, the resulting class of processes admits a wide range of behavior that includes both long memory, semi-long memory, and short memory processes. The paper develops asymptotic theory for such processes and associated regression statistics thereby extending earlier findings that fall within certain subclasses of processes involving near-integrated time series. The limit results relate to tempered fractional processes that include tempered fractional Brownian motion and tempered fractional diffusions of the second kind. The theory is extended to provide the limiting distribution for autoregressions with such tempered near-integrated time series, thereby enabling analysis of the limit properties of statistics of particular interest in econometrics, such as unit root tests, under more general conditions than existing theory. Some extensions of the theory to the multivariate case are reported.Effect of spatial correlation on stochastic resonance in two linearly interacting noisy bistable oscillators.https://www.zbmath.org/1456.601712021-04-16T16:22:00+00:00"Kang, Yan-Mei"https://www.zbmath.org/authors/?q=ai:kang.yanmei"Jiang, Jun"https://www.zbmath.org/authors/?q=ai:jiang.jun"Xie, Yong"https://www.zbmath.org/authors/?q=ai:xie.yongTesting serial correlations in high-dimensional time series via extreme value theory.https://www.zbmath.org/1456.622222021-04-16T16:22:00+00:00"Tsay, Ruey S."https://www.zbmath.org/authors/?q=ai:tsay.ruey-sSummary: This paper proposes a simple test for detecting serial correlations in high-dimensional time series. The proposed test makes use of the robust properties of Spearman's rank correlation and the theory of extreme values. Asymptotic properties of the test statistics are derived under some minor conditions as both the sample size and dimension go to infinity. The test is not sensitive to the underlying distribution of the time series so long as the data are continuously distributed. In particular, the existence of finite-order moments of the underlying distribution is not required, and asymptotic critical values of the test statistics are available in closed form. In finite samples, we correct biases of the sample autocorrelations and conduct simulations to study the performance of the proposed test statistics. Simulation results show that the proposed test statistics enjoy good properties of size and power in finite samples. We apply the proposed test to a 92-dimensional series of asset returns. Finally, a simple R code is available to obtain finite-sample critical values of the test statistics if needed.Smallest percolating sets in bootstrap percolation on grids.https://www.zbmath.org/1456.602642021-04-16T16:22:00+00:00"Przykucki, Michał"https://www.zbmath.org/authors/?q=ai:przykucki.michal"Shelton, Thomas"https://www.zbmath.org/authors/?q=ai:shelton.thomasSummary: In this paper we fill in a fundamental gap in the extremal bootstrap percolation literature, by providing the first proof of the fact that for all \(d \geqslant 1\), the size of the smallest percolating sets in \(d\)-neighbour bootstrap percolation on \([n]^d\), the \(d\)-dimensional grid of size \(n\), is \(n^{d-1}\). Additionally, we prove that such sets percolate in time at most \(c_d n^2\), for some constant \(c_d >0\) depending on \(d\) only.Fixation and escape times in stochastic game learning.https://www.zbmath.org/1456.910162021-04-16T16:22:00+00:00"Realpe-Gomez, John"https://www.zbmath.org/authors/?q=ai:realpe-gomez.john"Szczesny, Bartosz"https://www.zbmath.org/authors/?q=ai:szczesny.bartosz"Dall'Asta, Luca"https://www.zbmath.org/authors/?q=ai:dallasta.luca"Galla, Tobias"https://www.zbmath.org/authors/?q=ai:galla.tobiasTransient dynamics of a polymer in the start-up of linear-mixed flow.https://www.zbmath.org/1456.371012021-04-16T16:22:00+00:00"Dua, Arti"https://www.zbmath.org/authors/?q=ai:dua.artiCentral limit theorem for statistics of subcritical configuration models.https://www.zbmath.org/1456.600582021-04-16T16:22:00+00:00"Athreya, Siva"https://www.zbmath.org/authors/?q=ai:athreya.siva-r"Yogeshwaran, D."https://www.zbmath.org/authors/?q=ai:yogeshwaran.dhandapaniSummary: We consider subcritical configuration models and show that the central limit theorem for any additive statistic holds when the statistic satisfies a fourth moment assumption, a variance lower bound and the degree sequence of the graph satisfies a growth condition. If the degree sequence is bounded, for well known statistics like component counts, log-partition function, and maximum cut-size which are Lipschitz under addition of an edge or switchings then the assumptions reduce to a linear growth condition for the variance of the statistic. Our proof is based on an application of the central limit theorem for martingale-difference arrays due to
\textit{D. L. McLeish} [Ann. Probab. 2, 620--628 (1974; Zbl 0287.60025)] to a suitable exploration process.Discovering link communities in complex networks by exploiting link dynamics.https://www.zbmath.org/1456.910942021-04-16T16:22:00+00:00"He, Dongxiao"https://www.zbmath.org/authors/?q=ai:he.dongxiao"Liu, Dayou"https://www.zbmath.org/authors/?q=ai:liu.dayou"Zhang, Weixiong"https://www.zbmath.org/authors/?q=ai:zhang.weixiong"Jin, Di"https://www.zbmath.org/authors/?q=ai:jin.di"Yang, Bo"https://www.zbmath.org/authors/?q=ai:yang.bo.5Multiscale functional inequalities in probability: concentration properties.https://www.zbmath.org/1456.600532021-04-16T16:22:00+00:00"Duerinckx, Mitia"https://www.zbmath.org/authors/?q=ai:duerinckx.mitia"Gloria, Antoine"https://www.zbmath.org/authors/?q=ai:gloria.antoineSummary: In a companion article we have introduced a notion of multiscale functional inequalities for functions \(X(A)\) of an ergodic stationary random field \(A\) on the ambient space \(\mathbb{R}^d\). These inequalities are multiscale weighted versions of standard Poincaré, covariance, and logarithmic Sobolev inequalities. They hold for all the examples of fields \(A\) arising in the modelling of heterogeneous materials in the applied sciences whereas their standard versions are much more restrictive. In this contribution we first investigate the link between multiscale functional inequalities and more standard decorrelation or mixing properties of random fields. Next, we show that multiscale functional inequalities imply fine concentration properties for nonlinear functions \(X(A)\). This constitutes the main stochastic ingredient to the quenched large-scale regularity theory for random elliptic operators by the second author, Neukamm, and Otto [\textit{A. Gloria} et al., Milan J. Math. 88, No. 1, 99--170 (2020; Zbl 1440.35064)], and to the corresponding quantitative stochastic homogenization results.Local probabilities of randomly stopped sums of power-law lattice random variables.https://www.zbmath.org/1456.601012021-04-16T16:22:00+00:00"Bloznelis, Mindaugas"https://www.zbmath.org/authors/?q=ai:bloznelis.mindaugasSummary: Let \(X_1\) and \(N \geq 0\) be integer-valued power-law random variables. For a randomly stopped sum \(S_N = X_1+\cdots+X_N\) of independent and identically distributed copies of \(X_1\), we establish a first-order asymptotics of the local probabilities \(\mathbf{P}(S_N = t)\) as \(t \rightarrow + \infty \). Using this result, we show the scaling \(k^{- \delta }\), \(0 \leq \delta \leq 1\), of the local clustering coefficient (of a randomly selected vertex of degree \(k)\) in a power-law affiliation network.On the number of \(k\)-cycles in the assignment problem for random matrices.https://www.zbmath.org/1456.824982021-04-16T16:22:00+00:00"Esteve, José G."https://www.zbmath.org/authors/?q=ai:esteve.jose-g"Falceto, Fernando"https://www.zbmath.org/authors/?q=ai:falceto.fernandoCache miss estimation for non-stationary request processes.https://www.zbmath.org/1456.680202021-04-16T16:22:00+00:00"Olmos, Felipe"https://www.zbmath.org/authors/?q=ai:olmos.felipe"Graham, Carl"https://www.zbmath.org/authors/?q=ai:graham.carl"Simonian, Alain"https://www.zbmath.org/authors/?q=ai:simonian.alain-dSummary: The goal of the paper is to evaluate the miss probability of a Least Recently Used (LRU) cache, when it is offered a non-stationary request process given by a Poisson cluster point process. First, we construct a probability space using Palm theory, describing how to consider a tagged document with respect to the rest of the request process. This framework allows us to derive a fundamental integral formula for the expected number of misses of the tagged document. Then, we consider the limit when the cache size and the arrival rate go to infinity in proportion, and use the integral formula to derive an asymptotic expansion of the miss probability in powers of the inverse of the cache size. This enables us to quantify and improve the accuracy of the so-called \textit{Che approximation}.Non-existence of bi-infinite geodesics in the exponential corner growth model.https://www.zbmath.org/1456.602482021-04-16T16:22:00+00:00"Balázs, Márton"https://www.zbmath.org/authors/?q=ai:balazs.marton.1"Busani, Ofer"https://www.zbmath.org/authors/?q=ai:busani.ofer"Seppäläinen, Timo"https://www.zbmath.org/authors/?q=ai:seppalainen.timoSummary: This paper gives a self-contained proof of the non-existence of nontrivial bi-infinite geodesics in directed planar last-passage percolation with exponential weights. The techniques used are couplings, coarse graining, and control of geodesics through planarity and estimates derived from increment-stationary versions of the last-passage percolation process.Non-differentiable large-deviation functionals in boundary-driven diffusive systems.https://www.zbmath.org/1456.827152021-04-16T16:22:00+00:00"Bunin, Guy"https://www.zbmath.org/authors/?q=ai:bunin.guy"Kafri, Yariv"https://www.zbmath.org/authors/?q=ai:kafri.yariv"Podolsky, Daniel"https://www.zbmath.org/authors/?q=ai:podolsky.danielThe Pearson walk with shrinking steps in two dimensions.https://www.zbmath.org/1456.824492021-04-16T16:22:00+00:00"Serino, C. A."https://www.zbmath.org/authors/?q=ai:serino.c-a"Redner, S."https://www.zbmath.org/authors/?q=ai:redner.sidneyModelling large timescale and small timescale service variability.https://www.zbmath.org/1456.602462021-04-16T16:22:00+00:00"Gribaudo, Marco"https://www.zbmath.org/authors/?q=ai:gribaudo.marco"Horváth, Illés"https://www.zbmath.org/authors/?q=ai:horvath.illes"Manini, Daniele"https://www.zbmath.org/authors/?q=ai:manini.daniele"Telek, Miklós"https://www.zbmath.org/authors/?q=ai:telek.miklosSummary: The performance of service units may depend on various randomly changing environmental effects. It is quite often the case that these effects vary on different timescales. In this paper, we consider small and large scale (short and long term) service variability, where the short term variability affects the instantaneous service speed of the service unit and a modulating background Markov chain characterizes the long term effect. The main modelling challenge in this work is that the considered small and long term variation results in randomness along different axes: short term variability along the time axis and long term variability along the work axis. We present a simulation approach and an explicit analytic formula for the service time distribution in the double transform domain that allows for the efficient computation of service time moments. Finally, we compare the simulation results with analytic ones.Spin interfaces in the Ashkin-Teller model and SLE.https://www.zbmath.org/1456.821392021-04-16T16:22:00+00:00"Ikhlef, Y."https://www.zbmath.org/authors/?q=ai:ikhlef.yacine"Rajabpour, M. A."https://www.zbmath.org/authors/?q=ai:rajabpour.mohammad-aliPartitions into distinct parts with bounded largest part.https://www.zbmath.org/1456.050092021-04-16T16:22:00+00:00"Bridges, Walter"https://www.zbmath.org/authors/?q=ai:bridges.walterSummary: We prove an asymptotic formula for the number of partitions of \(n\) into distinct parts where the largest part is at most \(t\sqrt{n}\) for fixed \(t\in\mathbb{R}\). Our method follows a probabilistic approach of \textit{D. Romik} [Eur. J. Comb. 26, No. 1, 1--17 (2005; Zbl 1066.05020)], who gave a simpler proof of Szekeres' asymptotic formula for distinct parts partitions when instead the number of parts is bounded by \(t\sqrt{n}\). Although equivalent to a circle method/saddle-point method calculation, the probabilistic approach motivates some of the more technical steps and even predicts the shape of the asymptotic formula, to some degree.Infinitely ramified point measures and branching Lévy processes.https://www.zbmath.org/1456.602252021-04-16T16:22:00+00:00"Bertoin, Jean"https://www.zbmath.org/authors/?q=ai:bertoin.jean"Mallein, Bastien"https://www.zbmath.org/authors/?q=ai:mallein.bastienIn analogy to the well-known relation between infinitely divisible distributions and processes with stationary independent increments (Lévy processes), the authors connect what they call infinitely ramified point measures (IRPM) with branching Lévy processes (BLP). An IRPM is defined as a random point measure \(\mathcal{Z}\) which for every \(n\in\mathbb{N}\) has the same distribution as the \(n\)th generation of some branching random walk. In the considered BLP, particles move independently according to Lévy process and produce progeny during their lifetime similarly as in a Crump-Mode-Jagers branching process. The point measures, random walks and Lévy processes are taken here on the real line. Denote
\(\langle\Sigma_n \delta_{x_n},f\rangle:= \Sigma_n f(x_n)\) and \(\textbf{e}_\theta(x) :=\textbf{e}^{x\theta}\), \(\theta\ge 0\), \(x\in\mathbb{R}\). It is shown that given an IRPM \(\mathcal{Z}\) such that
(*) \(0< E(\langle\mathcal{Z}, \textbf{e}_\theta\rangle)<\infty\)
for some \(\theta\ge 0\), there exists a BLP \(Z= \{Z_t; t\ge 0\}\) with \(\mathcal{Z}\overset{(d)}{=} Z_1\). Vice versa, if \(Z\) is a BLP such that the corresponding Lévy measure satisfies certain integrability conditions, then \(Z_1\) is an IRPM satisfying (*).
Reviewer: Heinrich Hering (Rockenberg)Joint law of an Ornstein-Uhlenbeck process and its supremum.https://www.zbmath.org/1456.601992021-04-16T16:22:00+00:00"Blanchet-Scalliet, Christophette"https://www.zbmath.org/authors/?q=ai:blanchet-scalliet.christophette"Dorobantu, Diana"https://www.zbmath.org/authors/?q=ai:dorobantu.diana"Gay, Laura"https://www.zbmath.org/authors/?q=ai:gay.lauraSummary: Let \(X\) be an Ornstein-Uhlenbeck process driven by a Brownian motion. We propose an expression for the joint density/distribution function of the process and its running supremum. This law is expressed as an expansion involving parabolic cylinder functions. Numerically, we obtain this law faster with our expression than with a Monte Carlo method. Numerical applications illustrate the interest of this result.On the limit theory of mixed to unity VARs: panel setting with weakly dependent errors.https://www.zbmath.org/1456.622182021-04-16T16:22:00+00:00"Stauskas, Ovidijus"https://www.zbmath.org/authors/?q=ai:stauskas.ovidijusThe author of the paper considers a panel version of the bivariate vector autoregressive model. According to such model
\[
\mathbf{x}_{i,t}=\mathbf{R}_T\mathbf{x}_{i,t-1}+\mathbf{u}_{i,t},
\]
for \(t=1,\ldots, T\) and \(i=1,\dots,N\), where \(\mathbf{x}_{i,t}=\left({x}_{1,i,t},{x}_{2,i,t}\right)^\intercal\),
\(\mathbf{u}_{i,t}=\left({u}_{1,i,t},{u}_{2,i,t}\right)^\intercal\) and \(\mathbf{R}_T\) is a diagonal matrix with elements \(\rho_T\) and \(\theta_T\) on the diagonal. The coefficients \(\rho_T\), \(\theta_T\) represent local to unity, and author of the paper suppose that
\[
\rho_T=1+\frac{c}{T},\ \theta_T=1+\frac{b}{k_T},
\]
where \(c<0\), \(b>0\) and \(k_T=o(T)\).
The author of the paper considers asymptotic properties of the Wald test statistics for the hypothesis \(H_0: \mathbf{R}_T=\rho_T \mathbf{I}_2\). The derived assertions complement results of the paper [\textit{P. Phillips} and \textit{J.H. Lee}, Econometric Reviews 34, 1035--1056 (2015)].
Reviewer: Jonas Šiaulys (Vilnius)On the number of weakly connected subdigraphs in random \(k\)NN digraphs.https://www.zbmath.org/1456.050792021-04-16T16:22:00+00:00"Bahadır, Selim"https://www.zbmath.org/authors/?q=ai:bahadir.selim"Ceyhan, Elvan"https://www.zbmath.org/authors/?q=ai:ceyhan.elvanSummary: We study the number of copies of a weakly connected subdigraph of the \(k\) nearest neighbor \((k\)NN) digraph based on data from certain random point processes in \(\mathbb{R}^d\). In particular, based on the asymptotic theory for functionals of point sets from homogeneous Poisson process (HPP) and uniform binomial process (UBP), we provide a general result for the asymptotic behavior of the number of weakly connected subdigraphs of \(k\) NN digraphs. As corollaries, we obtain asymptotic results for the number of vertices with fixed indegree, the number of shared \(k\)NN pairs, and the number of reflexive \(k\)NNs in the \(k\)NN digraph based on data from HPP and UBP. We also provide several extensions of our results pertaining to the \(k\)NN digraphs; more specifically, the results are extended to the number of weakly connected subdigraphs in a digraph based only on a subset of the first \(k\)NNs, and in a marked or labeled digraph where each vertex also has a mark or a label associated with it, and also to the number of subgraphs of the underlying \(k\)NN graphs. These constructs derived from \(k\)NN digraphs, \(k\)NN graphs, and the marked/labeled \(k\)NN graphs have applications in various fields such as pattern classification and spatial data analysis, and our extensions provide the theoretical basis for certain tools in these areas.Analyzing the models of systems with heterogeneous servers.https://www.zbmath.org/1456.602452021-04-16T16:22:00+00:00"Melikov, A. Z."https://www.zbmath.org/authors/?q=ai:melikov.agassi-z"Ponomarenko, L. A."https://www.zbmath.org/authors/?q=ai:ponomarenko.leonid-a"Mekhbaliyeva, E. V."https://www.zbmath.org/authors/?q=ai:mekhbalyeva.e-vSummary: The mathematical model of a queueing system with heterogeneous servers, without queues, and with two types of requests is investigated. High-priority requests are processed in fast servers while low-priority calls are processed in slow servers. If all servers in some group are busy, then reassigning of requests to another group is allowed. Reassigning is based on random schemes and reassignment probability depends on the number of busy servers in appropriate group. Exact and approximate methods are developed for the analysis of characteristics of the system. Explicit approximate formulas to calculate the approximate values of characteristics are proposed.Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory.https://www.zbmath.org/1456.820792021-04-16T16:22:00+00:00"Torquato, Salvatore"https://www.zbmath.org/authors/?q=ai:torquato.salvatore"Scardicchio, A."https://www.zbmath.org/authors/?q=ai:scardicchio.antonello"Zachary, Chase E."https://www.zbmath.org/authors/?q=ai:zachary.chase-eIntegral fluctuation relations for entropy production at stopping times.https://www.zbmath.org/1456.600962021-04-16T16:22:00+00:00"Neri, Izaak"https://www.zbmath.org/authors/?q=ai:neri.izaak"Roldán, Édgar"https://www.zbmath.org/authors/?q=ai:roldan.edgar"Pigolotti, Simone"https://www.zbmath.org/authors/?q=ai:pigolotti.simone"Jülicher, Frank"https://www.zbmath.org/authors/?q=ai:julicher.frankPhase transition in a random minima model: mean field theory and exact solution on the Bethe lattice.https://www.zbmath.org/1456.823862021-04-16T16:22:00+00:00"Sollich, Peter"https://www.zbmath.org/authors/?q=ai:sollich.peter"Majumdar, Satya N."https://www.zbmath.org/authors/?q=ai:majumdar.satya-n"Bray, Alan J."https://www.zbmath.org/authors/?q=ai:bray.alan-jModeling of epidemic spreading on multilayer networks in uncertain environments.https://www.zbmath.org/1456.921382021-04-16T16:22:00+00:00"Jiang, Jian"https://www.zbmath.org/authors/?q=ai:jiang.jian"Liang, Junhao"https://www.zbmath.org/authors/?q=ai:liang.junhao"Zhou, Tianshou"https://www.zbmath.org/authors/?q=ai:zhou.tianshouQuantum statistics in network geometry with fractional flavor.https://www.zbmath.org/1456.814832021-04-16T16:22:00+00:00"Cinardi, Nicola"https://www.zbmath.org/authors/?q=ai:cinardi.nicola"Rapisarda, Andrea"https://www.zbmath.org/authors/?q=ai:rapisarda.andrea"Bianconi, Ginestra"https://www.zbmath.org/authors/?q=ai:bianconi.ginestraSquare functions for noncommutative differentially subordinate martingales.https://www.zbmath.org/1456.460522021-04-16T16:22:00+00:00"Jiao, Yong"https://www.zbmath.org/authors/?q=ai:jiao.yong"Randrianantoanina, Narcisse"https://www.zbmath.org/authors/?q=ai:randrianantoanina.narcisse"Wu, Lian"https://www.zbmath.org/authors/?q=ai:wu.lian"Zhou, Dejian"https://www.zbmath.org/authors/?q=ai:zhou.dejianSummary: We prove inequalities involving noncommutative differentially subordinate martingales. More precisely, we prove that if \(x\) is a self-adjoint noncommutative martingale and \(y\) is weakly differentially subordinate to \(x\) then \(y\) admits a decomposition \(dy = a + b + c\) (resp. \( dy = z + w)\) where \(a, b\), and \(c\) are adapted sequences (resp., \(z\) and \(w\) are martingale difference sequences) such that:
\[ \| (a_n)_{n \geq 1} \|_{L_{1, \infty} (\mathcal{M} \overline{\otimes} \ell_{\infty})} + \left\| \left(\sum_{n \geq 1} \mathcal{E}_{n-1} |b_n |^2 \right)^{1/2} \right\|_{1, \infty}
+ \left\| \left(\sum_{n \geq 1} \mathcal{E}_{n-1} |c_n^* |^2 \right)^{1/2} \right\|_{1, \infty} \leq C \| x \|_1
\]
\[
\text{(resp., } \left\| \left(\sum_{n \geq 1} |z_n|^2 \right)^{{1}/{2}}\right\|_{1, \infty}+ \left\| \left(\sum_{n \geq 1} |w_n^*|^2 \right)^{1/2} \right\|_{1, \infty} \leq C \| x \|_1).
\]
We also prove strong-type \((p,p)\) versions of the above weak-type results for \(1 < p < 2\). In order to provide more insights into the interactions between noncommutative differential subordinations and martingale Hardy spaces when \(1 \leq p < 2\), we also provide several martingale inequalities with sharp constants which are new and of independent interest. As a byproduct of our approach, we obtain new and constructive proofs of both the noncommutative Burkholder-Gundy inequalities and the noncommutative Burkholder/Rosenthal inequalities for \(1 < p < 2\) with the optimal order of the constants when \(p \to 1\).Weakly mixing smooth planar vector field without asymptotic directions.https://www.zbmath.org/1456.370032021-04-16T16:22:00+00:00"Bakhtin, Yuri"https://www.zbmath.org/authors/?q=ai:bakhtin.yuri-yu"Li, Liying"https://www.zbmath.org/authors/?q=ai:li.liyingBased on the work [\textit{J. Chaika} and \textit{A. Krishnan}, Probab. Theory Relat. Fields 175, No. 3--4, 655--675 (2019; Zbl 1434.37004)], where the construction of a discrete \(\mathbb{Z}^2\)-ergodic example is provided, a planar smooth weakly mixing stationary random vector field with non-negative components is here constructed by appropriate tilings, smoothing, and randomization. The random flow possesses some interesting dynamical behavior: it does not have an asymptotic direction and the set of partial limiting directions spans the positive quadrant.
Reviewer: Xu Zhang (Weihai)Hausdorff dimension of limsup sets of rectangles in the Heisenberg group.https://www.zbmath.org/1456.600382021-04-16T16:22:00+00:00"Ekström, Fredrik"https://www.zbmath.org/authors/?q=ai:ekstrom.fredrik"Järvenpää, Esa"https://www.zbmath.org/authors/?q=ai:jarvenpaa.esa"Järvenpää, Maarit"https://www.zbmath.org/authors/?q=ai:jarvenpaa.maaritThe main findings of the paper refer to computing the almost sure value of the Hausdorff dimension of limsup sets generated by randomly distributed rectangles in the Heisenberg group, in terms of directed singular value functions.
Reviewer: George Stoica (Saint John)Book review of: R. L. Schilling, Wahrscheinlichkeit.https://www.zbmath.org/1456.000412021-04-16T16:22:00+00:00"Teschl, G."https://www.zbmath.org/authors/?q=ai:teschl.geraldReview of [Zbl 1416.60005].Density profiles of the exclusive queuing process.https://www.zbmath.org/1456.602472021-04-16T16:22:00+00:00"Arita, Chikashi"https://www.zbmath.org/authors/?q=ai:arita.chikashi"Schadschneider, Andreas"https://www.zbmath.org/authors/?q=ai:schadschneider.andreasA new type of critical behaviour in random matrix models.https://www.zbmath.org/1456.825002021-04-16T16:22:00+00:00"Flume, R."https://www.zbmath.org/authors/?q=ai:flume.rainald"Klitz, A."https://www.zbmath.org/authors/?q=ai:klitz.alexander(no abstract)Global properties of stochastic Loewner evolution driven by Lévy processes.https://www.zbmath.org/1456.827832021-04-16T16:22:00+00:00"Oikonomou, P."https://www.zbmath.org/authors/?q=ai:oikonomou.p"Rushkin, I."https://www.zbmath.org/authors/?q=ai:rushkin.i"Gruzberg, I. A."https://www.zbmath.org/authors/?q=ai:gruzberg.ilya-a"Kadanoff, L. P."https://www.zbmath.org/authors/?q=ai:kadanoff.leo-pTopological estimation of percolation thresholds.https://www.zbmath.org/1456.824722021-04-16T16:22:00+00:00"Neher, Richard A."https://www.zbmath.org/authors/?q=ai:neher.richard-a"Mecke, Klaus"https://www.zbmath.org/authors/?q=ai:mecke.klaus-r"Wagner, Herbert"https://www.zbmath.org/authors/?q=ai:wagner.herbert.1Equilibrium and termination.https://www.zbmath.org/1456.680712021-04-16T16:22:00+00:00"Danos, Vincent"https://www.zbmath.org/authors/?q=ai:danos.vincent"Oury, Nicolas"https://www.zbmath.org/authors/?q=ai:oury.nicolasSummary: We present a reduction of the termination problem for a Turing machine (in the simplified form of the Post correspondence problem) to the problem of determining whether a continuous-time Markov chain presented as a set of Kappa graph-rewriting rules has an equilibrium. It follows that the problem of whether a computable CTMC is dissipative (ie does not have an equilibrium) is undecidable.
For the entire collection see [Zbl 1445.68010].Piecewise deterministic Markov processes driven by scalar conservation laws.https://www.zbmath.org/1456.601872021-04-16T16:22:00+00:00"Knapp, Stephan"https://www.zbmath.org/authors/?q=ai:knapp.stephanSummary: We investigate piecewise deterministic Markov processes (PDMP), where the deterministic dynamics follows a scalar conservation law and random jumps in the system are characterized by changes in the flux function. We show under which assumptions we can guarantee the existence of a PDMP and conclude bounded variation estimates for sample paths. Finally, we apply this dynamics to a production and traffic model and use this framework to incorporate the well-known scattering of flux functions observed in data sets.
For the entire collection see [Zbl 1453.35003].Non-Gaussian features of chaotic Hamiltonian transport.https://www.zbmath.org/1456.370392021-04-16T16:22:00+00:00"Venegeroles, Roberto"https://www.zbmath.org/authors/?q=ai:venegeroles.roberto"Saa, Alberto"https://www.zbmath.org/authors/?q=ai:saa.albertoOn the convergence and regularity of Aumann-Pettis integrable multivalued martingales.https://www.zbmath.org/1456.600972021-04-16T16:22:00+00:00"El Allali, Mohammed"https://www.zbmath.org/authors/?q=ai:el-allali.mohammed"El-Louh, M'hamed"https://www.zbmath.org/authors/?q=ai:el-louh.mhamed"Ezzaki, Fatima"https://www.zbmath.org/authors/?q=ai:ezzaki.fatimaSummary: We prove a representation of Aumann-Pettis integrable multivalued martingales by Pettis integrable martingale selectors. Regularity of Aumann-Pettis integrable multivalued martingales and their convergence in Mosco sense, Wijsman topology, and linear topology are established.Multivalued strong laws of large numbers for triangular arrays with gap topology.https://www.zbmath.org/1456.600682021-04-16T16:22:00+00:00"Giap, Duong Xuan"https://www.zbmath.org/authors/?q=ai:giap.duong-xuan"van Huan, Nguyen"https://www.zbmath.org/authors/?q=ai:van-huan.nguyen"Ngoc, Bui Nguyen Tram"https://www.zbmath.org/authors/?q=ai:ngoc.bui-nguyen-tram"van Quang, Nguyen"https://www.zbmath.org/authors/?q=ai:quang.nguyen-vanSummary: We state some strong laws of large numbers for triangular arrays of random sets in separable Banach spaces with the gap topology and with or without compactly uniformly integrable condition.Geometry of \(\ell_p^n\)-balls: classical results and recent developments.https://www.zbmath.org/1456.460132021-04-16T16:22:00+00:00"Prochno, Joscha"https://www.zbmath.org/authors/?q=ai:prochno.joscha"Thäle, Christoph"https://www.zbmath.org/authors/?q=ai:thale.christoph"Turchi, Nicola"https://www.zbmath.org/authors/?q=ai:turchi.nicolaSummary: In this article we first review some by-now classical results about the geometry of \(\ell_p\)-balls \(\mathbb{B}_p^n\) in \(\mathbb{R}^n\) and provide modern probabilistic arguments for them. We also present some more recent developments including a central limit theorem and a large deviations principle for the \(q\)-norm of a random point in \(\mathbb{B}_p^n\). We discuss their relation to the classical results and give hints to various extensions that are available in the existing literature.
For the entire collection see [Zbl 1431.60003].Asymptotic statistics of the \(n\)-sided planar Poisson-Voronoi cell. I: Exact results.https://www.zbmath.org/1456.600402021-04-16T16:22:00+00:00"Hilhorst, H. J."https://www.zbmath.org/authors/?q=ai:hilhorst.hendrik-janAnisotropic KPZ growth in 2+1 dimensions: fluctuations and covariance structure.https://www.zbmath.org/1456.827142021-04-16T16:22:00+00:00"Borodin, Alexei"https://www.zbmath.org/authors/?q=ai:borodin.alexei"Ferrari, Patrik L."https://www.zbmath.org/authors/?q=ai:ferrari.patrik-linoPosition-momentum decomposition of linear operators defined on algebras of polynomials.https://www.zbmath.org/1456.812692021-04-16T16:22:00+00:00"Stan, A. I."https://www.zbmath.org/authors/?q=ai:stan.aurel-iulian"Popa, G."https://www.zbmath.org/authors/?q=ai:popa.gabriela"Dutta, R."https://www.zbmath.org/authors/?q=ai:dutta.ritik|dutta.ramya|dutta.ritabrata|dutta.rajib|dutta.ratan-kumar|dutta.ratna|dutta.rajdeep|dutta.roy-s-c|dutta.rudra|dutta.r-n|dutta.rahul|dutta.rohanSummary: We present first a set of commutator relationships involving the joint quantum, semi-quantum, and number operators generated by a finite family of random variables, having finite moments of all orders, and show how these commutators can be used to recover the joint quantum operators from the semi-quantum operators. We show that any linear operator defined on an algebra of polynomials or the polynomial random variables, generated by a finite family of random variables, having finite moments of all orders, can be written uniquely as an infinite sum of compositions of the multiplication operators, generated by these random variables, and the partial derivative operators. In the terms of this sum, each multiplication operator is placed to the left side of each partial derivative operator. We provide many examples concerning the decomposition of some classic operators.
{\copyright 2021 American Institute of Physics}Inhomogeneous percolation models for spreading phenomena in random graphs.https://www.zbmath.org/1456.824592021-04-16T16:22:00+00:00"Dall'Asta, Luca"https://www.zbmath.org/authors/?q=ai:dallasta.lucaThe convex hull of the run-and-tumble particle in a plane.https://www.zbmath.org/1456.601052021-04-16T16:22:00+00:00"Hartmann, Alexander K."https://www.zbmath.org/authors/?q=ai:hartmann.alexander-k"Majumdar, Satya N."https://www.zbmath.org/authors/?q=ai:majumdar.satya-n"Schawe, Hendrik"https://www.zbmath.org/authors/?q=ai:schawe.hendrik"Schehr, Grégory"https://www.zbmath.org/authors/?q=ai:schehr.gregoryDriven tracers in a one-dimensional periodic hard-core lattice gas.https://www.zbmath.org/1456.602612021-04-16T16:22:00+00:00"Lobaskin, Ivan"https://www.zbmath.org/authors/?q=ai:lobaskin.ivan"Evans, Martin R."https://www.zbmath.org/authors/?q=ai:evans.martin-rVertex models and random labyrinths: phase diagrams for ice-type vertex models.https://www.zbmath.org/1456.821882021-04-16T16:22:00+00:00"Shtengel, Kirill"https://www.zbmath.org/authors/?q=ai:shtengel.kirill"Chayes, L. P."https://www.zbmath.org/authors/?q=ai:chayes.l-pThe optimal edge for containing the spreading of SIS model.https://www.zbmath.org/1456.921472021-04-16T16:22:00+00:00"Xian, Jiajun"https://www.zbmath.org/authors/?q=ai:xian.jiajun"Yang, Dan"https://www.zbmath.org/authors/?q=ai:yang.dan"Pan, Liming"https://www.zbmath.org/authors/?q=ai:pan.liming"Wang, Wei"https://www.zbmath.org/authors/?q=ai:wang.wei.30About the foundation of the Kubo generalized cumulants theory: a revisited and corrected approach.https://www.zbmath.org/1456.600472021-04-16T16:22:00+00:00"Bianucci, Marco"https://www.zbmath.org/authors/?q=ai:bianucci.marco"Bologna, Mauro"https://www.zbmath.org/authors/?q=ai:bologna.mauroPeriodic solutions of a periodic stochastic human immunodeficiency virus model with distributed delay and cytotoxic T lymphocytes immune response.https://www.zbmath.org/1456.920812021-04-16T16:22:00+00:00"Hou, Yuying"https://www.zbmath.org/authors/?q=ai:hou.yuying"Shi, Peilin"https://www.zbmath.org/authors/?q=ai:shi.peilinSummary: In this paper, a periodic stochastic human immunodeficiency virus (HIV) model with distributed delay and cytotoxic T lymphocytes (CTL) immune response is investigated. First, by Itô's formula, we show that the solution with any positive initial value is global and positive. Then, by the stochastic comparison theorem, we obtain the sufficient conditions guaranteeing the existence and global attractivity of infection-free periodic solution. Furthermore, we discuss the existence of the infective periodic solution by Has'minskii theory. Finally, numerical examples are given to illustrate the results.The role of dynamic defects in transport of interacting molecular motors.https://www.zbmath.org/1456.920242021-04-16T16:22:00+00:00"Jindal, Akriti"https://www.zbmath.org/authors/?q=ai:jindal.akriti"Kolomeisky, Anatoly B."https://www.zbmath.org/authors/?q=ai:kolomeisky.anatoly-b"Gupta, Arvind Kumar"https://www.zbmath.org/authors/?q=ai:gupta.arvind-kumarConservation laws for voter-like models on random directed networks.https://www.zbmath.org/1456.826402021-04-16T16:22:00+00:00"Ángeles Serrano, M."https://www.zbmath.org/authors/?q=ai:serrano.m-angeles"Klemm, Konstantin"https://www.zbmath.org/authors/?q=ai:klemm.konstantin"Vazquez, Federico"https://www.zbmath.org/authors/?q=ai:vazquez.federico"Eguíluz, Víctor M."https://www.zbmath.org/authors/?q=ai:eguiluz.victor-m"San Miguel, Maxi"https://www.zbmath.org/authors/?q=ai:miguel.maxi-sanRare events in stochastic processes with sub-exponential distributions and the big jump principle.https://www.zbmath.org/1456.601242021-04-16T16:22:00+00:00"Burioni, Raffaella"https://www.zbmath.org/authors/?q=ai:burioni.raffaella"Vezzani, Alessandro"https://www.zbmath.org/authors/?q=ai:vezzani.alessandroA growth-fragmentation model related to Ornstein-Uhlenbeck type processes.https://www.zbmath.org/1456.601172021-04-16T16:22:00+00:00"Shi, Quan"https://www.zbmath.org/authors/?q=ai:shi.quanSummary: Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we introduce a new type of growth-fragmentation which is closely related to Lévy driven Ornstein-Uhlenbeck type processes. Our model can be viewed as a generalization of compensated fragmentation processes introduced by Bertoin, or the stochastic counterpart of a family of growth-fragmentation equations. We establish a convergence criterion for a sequence of such growth-fragmentations. We also prove that, under certain conditions, this system fulfills a law of large numbers.A matrix model for plane partitions.https://www.zbmath.org/1456.824372021-04-16T16:22:00+00:00"Eynard, B."https://www.zbmath.org/authors/?q=ai:eynard.bertrandDynamics of a stochastic chemostat competition model with plasmid-bearing and plasmid-free organisms.https://www.zbmath.org/1456.920842021-04-16T16:22:00+00:00"Gao, Miaomiao"https://www.zbmath.org/authors/?q=ai:gao.miaomiao"Jiang, Daqing"https://www.zbmath.org/authors/?q=ai:jiang.daqing"Hayat, Tasawar"https://www.zbmath.org/authors/?q=ai:hayat.tasawar"Alsaedi, Ahmed"https://www.zbmath.org/authors/?q=ai:alsaedi.ahmed"Ahmad, Bashir"https://www.zbmath.org/authors/?q=ai:ahmad.bashir.2|ahmad.bashir.1Summary: In this paper, we consider a chemostat model of competition between plasmid-bearing and plasmid-free organisms, perturbed by white noise. Firstly, we prove the existence and uniqueness of the global positive solution. Then by constructing suitable Lyapunov functions, we establish sufficient conditions for the existence of a unique ergodic stationary distribution. Furthermore, conditions for extinction of plasmid-bearing organisms are obtained. Theoretical analysis indicates that large noise intensity \(\sigma_2^2\) is detrimental to the survival of plasmid-bearing organisms and is not conducive to the commercial production of genetically altered organisms. Finally, numerical simulations are presented to illustrate the results.Limit theorems for a stochastic model of adoption and abandonment innovation on homogeneously mixing populations.https://www.zbmath.org/1456.601932021-04-16T16:22:00+00:00"Oliveira, K. B. E."https://www.zbmath.org/authors/?q=ai:oliveira.k-b-e"Rodriguez, P. M."https://www.zbmath.org/authors/?q=ai:rodriguez.pablo-m|rodriguez.pedro-mFluctuations around a homogenised semilinear random PDE.https://www.zbmath.org/1456.352432021-04-16T16:22:00+00:00"Hairer, Martin"https://www.zbmath.org/authors/?q=ai:hairer.martin"Pardoux, Étienne"https://www.zbmath.org/authors/?q=ai:pardoux.etienneSummary: We consider a semilinear parabolic partial differential equation in \(\mathbb{R}_+ \times [0, 1]^d\), where \(d = 1, 2\) or 3, with a highly oscillating random potential and either homogeneous Dirichlet or Neumann boundary condition. If the amplitude of the oscillations has the right size compared to its typical spatiotemporal scale, then the solution of our equation converges to the solution of a deterministic homogenised parabolic PDE, which is a form of law of large numbers. Our main interest is in the associated central limit theorem. Namely, we study the limit of a properly rescaled difference between the initial random solution and its LLN limit. In dimension \(d = 1\), that rescaled difference converges as one might expect to a centred Ornstein-Uhlenbeck process. However, in dimension \(d = 2\), the limit is a non-centred Gaussian process, while in dimension \(d = 3\), before taking the CLT limit, we need to subtract at an intermediate scale the solution of a deterministic parabolic PDE, subject (in the case of Neumann boundary condition) to a non-homogeneous Neumann boundary condition. Our proofs make use of the theory of regularity structures, in particular of the very recently developed methodology allowing to treat parabolic PDEs with boundary conditions within that theory.Surface super-roughening driven by spatiotemporally correlated noise.https://www.zbmath.org/1456.352402021-04-16T16:22:00+00:00"Alés, Alejandro"https://www.zbmath.org/authors/?q=ai:ales.alejandro"López, Juan M."https://www.zbmath.org/authors/?q=ai:lopez.juan-manuel|lopez.juan-manuel.1|lopez.juan-mA microscopic model for a one parameter class of fractional Laplacians with Dirichlet boundary conditions.https://www.zbmath.org/1456.352102021-04-16T16:22:00+00:00"Bernardin, C."https://www.zbmath.org/authors/?q=ai:bernardin.cedric"Gonçalves, P."https://www.zbmath.org/authors/?q=ai:goncalves.patricia-c"Jiménez-Oviedo, B."https://www.zbmath.org/authors/?q=ai:jimenez-oviedo.bSummary: We prove the hydrodynamic limit for the symmetric exclusion process with long jumps given by a mean zero probability transition rate with infinite variance and in contact with infinitely many reservoirs with density \(\alpha\) at the left of the system and \(\beta\) at the right of the system. The strength of the reservoirs is ruled by \(\kappa N^{-\theta} > 0\). Here \(N\) is the size of the system, \(\kappa > 0\) and \(\theta \in \mathbb{R}\). Our results are valid for \(\theta \le 0\). For \(\theta = 0\), we obtain a collection of fractional reaction-diffusion equations indexed by the parameter \(\kappa\) and with Dirichlet boundary conditions. Their solutions also depend on \(\kappa\). For \(\theta < 0\), the hydrodynamic equation corresponds to a reaction equation with Dirichlet boundary conditions. The case \(\theta > 0\) is still open. For that reason we also analyze the convergence of the unique weak solution of the equation in the case \(\theta = 0\) when we send the parameter \(\kappa\) to zero. Indeed, we conjecture that the limiting profile when \(\kappa \rightarrow 0\) is the one that we should obtain when taking small values of \(\theta > 0\).Periodically driven jump processes conditioned on large deviations.https://www.zbmath.org/1456.601922021-04-16T16:22:00+00:00"Chabane, Lydia"https://www.zbmath.org/authors/?q=ai:chabane.lydia"Chétrite, Raphaël"https://www.zbmath.org/authors/?q=ai:chetrite.raphael"Verley, Gatien"https://www.zbmath.org/authors/?q=ai:verley.gatienOperator differential-algebraic equations with noise arising in fluid dynamics.https://www.zbmath.org/1456.650342021-04-16T16:22:00+00:00"Altmann, Robert"https://www.zbmath.org/authors/?q=ai:altmann.robert"Levajković, Tijana"https://www.zbmath.org/authors/?q=ai:levajkovic.tijana"Mena, Hermann"https://www.zbmath.org/authors/?q=ai:mena.hermannThe authors study linear stochastic operator differential algebraic equations (DAEs) that arise in fluid dynamics, notably the Stokes equation as a prototype. Deterministic regularization techniques are combined with polynomial chaos expansion methods to obtain explicit solutions. Existence and uniqueness of the solutions is proven in Kondratiev spaces of stochastic processes. The stochastic operator theoretical background of the paper relies on [\textit{T. Levajković} et al., Electron. J. Probab. 20, Paper No. 19, 23 p. (2015; Zbl 1321.60137)].
Reviewer: Dora Seleši (Novi Sad)Observation time dependent mean first passage time of diffusion and subdiffusion processes.https://www.zbmath.org/1456.602182021-04-16T16:22:00+00:00"Kim, Ji-Hyun"https://www.zbmath.org/authors/?q=ai:kim.jihyun|kim.ji-hyun"Lee, Hunki"https://www.zbmath.org/authors/?q=ai:lee.hunki"Song, Sanggeun"https://www.zbmath.org/authors/?q=ai:song.sanggeun"Koh, Hye Ran"https://www.zbmath.org/authors/?q=ai:koh.hye-ran"Sung, Jaeyoung"https://www.zbmath.org/authors/?q=ai:sung.jaeyoungCircles of equal radii randomly placed on a plane: some rigorous results, asymptotic behavior, and application to transparent electrodes.https://www.zbmath.org/1456.600362021-04-16T16:22:00+00:00"Akhunzhanov, R. K."https://www.zbmath.org/authors/?q=ai:akhunzhanov.renat-k"Tarasevich, Y. Y."https://www.zbmath.org/authors/?q=ai:tarasevich.yu-yu"Vodolazskaya, I. V."https://www.zbmath.org/authors/?q=ai:vodolazskaya.i-vDipolar stochastic Loewner evolutions.https://www.zbmath.org/1456.827132021-04-16T16:22:00+00:00"Bauer, M."https://www.zbmath.org/authors/?q=ai:bauer.martin.1|bauer.michael.1|bauer.michael.2|bauer.mariano|bauer.max|bauer.marcus|bauer.marco|bauer.michel|bauer.madeleine|bauer.maria|bauer.michael-a|bauer.mathias|bauer.matthias|bauer.manfred|bauer.martin.2|bauer.martin.3"Bernard, D."https://www.zbmath.org/authors/?q=ai:bernard.daniel|bernard.damien|bernard.douglas-e|bernard.denis"Houdayer, J."https://www.zbmath.org/authors/?q=ai:houdayer.jeromeOn the mean square displacement in Lévy walks.https://www.zbmath.org/1456.601112021-04-16T16:22:00+00:00"Börgers, Christoph"https://www.zbmath.org/authors/?q=ai:borgers.christoph"Greengard, Claude"https://www.zbmath.org/authors/?q=ai:greengard.claudeOn block Gaussian sketching for the Kaczmarz method.https://www.zbmath.org/1456.650232021-04-16T16:22:00+00:00"Rebrova, Elizaveta"https://www.zbmath.org/authors/?q=ai:rebrova.elizaveta"Needell, Deanna"https://www.zbmath.org/authors/?q=ai:needell.deannaSummary: The Kaczmarz algorithm is one of the most popular methods for solving large-scale over-determined linear systems due to its simplicity and computational efficiency. This method can be viewed as a special instance of a more general class of sketch and project methods. Recently, a block Gaussian version was proposed that uses a block Gaussian sketch, enjoying the regularization properties of Gaussian sketching, combined with the acceleration of the block variants. Theoretical analysis was only provided for the non-block version of the Gaussian sketch method. Here, we provide theoretical guarantees for the block Gaussian Kaczmarz method, proving a number of convergence results showing convergence to the solution exponentially fast in expectation. On the flip side, with this theory and extensive experimental support, we observe that the numerical complexity of each iteration typically makes this method inferior to other iterative projection methods. We highlight only one setting in which it may be advantageous, namely when the regularizing effect is used to reduce variance in the iterates under certain noise models and convergence for some particular matrix constructions.Fluctuation theorems and large-deviation functions in systems not featuring a steady state.https://www.zbmath.org/1456.812952021-04-16T16:22:00+00:00"Wio, Horacio S."https://www.zbmath.org/authors/?q=ai:wio.horacio-sergio"Deza, Roberto R."https://www.zbmath.org/authors/?q=ai:deza.roberto-raul"Revelli, Jorge A."https://www.zbmath.org/authors/?q=ai:revelli.jorge-aAsymptotic analysis of unstable solutions of stochastic differential equations.https://www.zbmath.org/1456.600022021-04-16T16:22:00+00:00"Kulinich, Grigorij"https://www.zbmath.org/authors/?q=ai:kulinich.grigorii-l"Kushnirenko, Svitlana"https://www.zbmath.org/authors/?q=ai:kushnirenko.svitlana-v"Mishura, Yuliya"https://www.zbmath.org/authors/?q=ai:mishura.yuliya-sSDEs (stochastic differential equations) is one of the main topics of modern probability theory and its applications. Usually we deal with a stochastic process, say \(X_t, \ t \geq 0\), obtained as a solution of a specific SDE and derive a series of `nice' properties of its distributions and trajectories. One of the fundamental questions of interest is: \ what is \ \(\lim_{t \to \infty}X_t.\) There are many results showing that, under appropriate conditions, \(\lim_{t \to \infty}X_t\) tends to zero, or belongs to a bounded domain in which case we say that the solution \(X_t, \ t \geq 0\) is stable. Of course, the stability property is specified in any concrete case.
Thus, if the SDE is such that in one or another sense the limit \(\lim_{t \to \infty}X_t\) is unbounded, we say the solution
\(X_t, t \geq 0\) is unstable. Studying unstable SDEs is not less important and not easier to deal with than studying stable SDEs. The present book is the first systematic account of most models, problems, results and ideas available in the literature.
One of the co-authors, Prof. G. Kulinich was the first who started studying unstable SDEs. The topic was suggested
to him by A.V. Skorokhod in 1965.
The material is well structured and distributed in six chapters. The main goal is to analyze appropriate integral functionals of unstable stochastic processes related to diverse sort of SDEs and establish limit theorems. The Brownian motion and Itô type of SDEs are essentially involved. A large number of results with specified kind of convergence is presented together with their proofs and illustrative examples. The limiting objects always have a simple structure, e.g., a constant, a proper random variable or a specific `easier' stochastic process. All limits are described in detail. Thus, to start with an unstable stochastic process and transform it into something easier and tractable is a successful way of a `domestication' of unstable stochastic processes. Important is to see `domesticated' limiting objects, all easy to work with.
The book ends with an appendix containing basic notions and results used intensively in the text and references of
both theoretical and applied nature. There is no index.
Besides their theoretical value, many of the results in this book are related to specific practical problems.
Specific indications are given in the text.
Some ideas and techniques exploited here can eventually be used or extended for studying other classes of
unstable stochastic processes.
The book will be of interest to anybody working in stochastic analysis and its applications, from master and PhD students
to professional researchers. Applied scientists can also benefit from this book by seeing efficient methods to
deal with unstable processes.
Reviewer: Jordan M. Stoyanov (Sofia)Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring.https://www.zbmath.org/1456.826452021-04-16T16:22:00+00:00"Banerjee, Tirthankar"https://www.zbmath.org/authors/?q=ai:banerjee.tirthankar"Sarkar, Niladri"https://www.zbmath.org/authors/?q=ai:sarkar.niladri"Basu, Abhik"https://www.zbmath.org/authors/?q=ai:basu.abhikReduction from non-Markovian to Markovian dynamics: the case of aging in the noisy-voter model.https://www.zbmath.org/1456.910482021-04-16T16:22:00+00:00"Peralta, Antonio F."https://www.zbmath.org/authors/?q=ai:peralta.antonio-f"Khalil, Nagi"https://www.zbmath.org/authors/?q=ai:khalil.nagi"Toral, Raúl"https://www.zbmath.org/authors/?q=ai:toral.raulMetastability of stochastic PDEs and Fredholm determinants.https://www.zbmath.org/1456.601572021-04-16T16:22:00+00:00"Berglund, Nils"https://www.zbmath.org/authors/?q=ai:berglund.nilsSummary: La métastabilité apparaît lorsqu'un système thermodynamique, tel que l'eau en surfusion (qui est liquide à température négative), se retrouve du ``mauvais'' côté d'une transition de phase, et reste pendant un temps très dans un état différent de son état d'équilibre. Il existe de nombreux modèles mathématiques décrivant ce phénomène, dont des modèles sur réseau à dynamique stochastique. Dans ce texte, nous allons nous intéresser à la métastabilité dans des équations aux dérivées partielles stochastiques (EDPS) paraboliques. Certaines de ces équations sont mal posées, et ce n'est que grâce à des progrès très récents dans la théorie des EDPS dites singulières qu'on sait construiere des solutions, via, une procédure de renormalisation. L'étude de la métastabilité dans ces systèmes fait apparaître des liens inattendus avec la théorie des déterminants spectraux, dont les déterminants de Fredholm et de Carleman-Fredholm.A stochastically perturbed mean curvature flow by colored noise.https://www.zbmath.org/1456.601642021-04-16T16:22:00+00:00"Yokoyama, Satoshi"https://www.zbmath.org/authors/?q=ai:yokoyama.satoshiSummary: We study the motion of the hypersurface \((\gamma_t)_{t\ge 0}\) evolving according to the mean curvature perturbed by \(\dot{w}^Q\), the formal time derivative of the \(Q\)-Wiener process \({w}^Q\), in a two-dimensional bounded domain. Namely, we consider the equation describing the evolution of \(\gamma_t\) as a stochastic partial differential equation (SPDE) with a multiplicative noise in the Stratonovich sense, whose inward velocity \(V\) is determined by \(V=\kappa+G\circ\dot{w}^Q\), where \(\kappa\) is the mean curvature and \(G\) is a function determined from \(\gamma_t\). Already known results in which the noise depends on only the time variable are not applicable to our equation. To construct a local solution of the equation describing \(\gamma_t\), we derive a certain second-order quasilinear SPDE with respect to the signed distance function determined from \(\gamma_0\). Then we construct the local solution making use of probabilistic tools and the classical Banach fixed point theorem on suitable Sobolev spaces.An \(L^p\) multiplicative coboundary theorem for sequences of unitriangular random matrices.https://www.zbmath.org/1456.600242021-04-16T16:22:00+00:00"Morrow, Steven T."https://www.zbmath.org/authors/?q=ai:morrow.steven-tSummary: \textit{R. C. Bradley} [ibid.. 9, No. 3, 659--678 (1996; Zbl 0870.60028)] proved a ``multiplicative coboundary'' theorem for sequences of unitriangular random matrices with integer entries, requiring tightness of the family of distributions of the entries from the partial matrix products of the sequence. This was an analog of \textit{K. Schmidt}'s result [Cocycles on ergodic transformation groups. Macmillan Lectures in Mathematics 1. Delhi, Bombay, Calcutta, Madras: The Macmillan Company of India Ltd. (1977; Zbl 0421.28017)] for sequences of real-valued random variables with tightness of the family of partial sums. Here is an \(L^p\) moment analog of Bradley's result which also relaxes the restriction of entries being integers.Existence and uniqueness results for time-inhomogeneous time-change equations and Fokker-Planck equations.https://www.zbmath.org/1456.351982021-04-16T16:22:00+00:00"Döring, Leif"https://www.zbmath.org/authors/?q=ai:doring.leif"Gonon, Lukas"https://www.zbmath.org/authors/?q=ai:gonon.lukas"Prömel, David J."https://www.zbmath.org/authors/?q=ai:promel.david-j"Reichmann, Oleg"https://www.zbmath.org/authors/?q=ai:reichmann.olegSummary: We prove existence and uniqueness of solutions to Fokker-Planck equations associated with Markov operators multiplicatively perturbed by degenerate time-inhomogeneous coefficients. Precise conditions on the time-inhomogeneous coefficients are given. In particular, we do not necessarily require the coefficients to be either globally bounded or bounded away from zero. The approach is based on constructing random time-changes and studying related martingale problems for Markov processes with values in locally compact, complete and separable metric spaces.Dynamic transition in a Brownian fluid: role of fluctuation-dissipation constraints.https://www.zbmath.org/1456.760962021-04-16T16:22:00+00:00"Das, Shankar P."https://www.zbmath.org/authors/?q=ai:das.shankar-pDispersion of the prehistory distribution for non-gradient systems.https://www.zbmath.org/1456.602232021-04-16T16:22:00+00:00"Zhu, Jinjie"https://www.zbmath.org/authors/?q=ai:zhu.jinjie"Wang, Jiong"https://www.zbmath.org/authors/?q=ai:wang.jiong"Gao, Shang"https://www.zbmath.org/authors/?q=ai:gao.shang"Liu, Xianbin"https://www.zbmath.org/authors/?q=ai:liu.xianbinRare events and scaling properties in field-induced anomalous dynamics.https://www.zbmath.org/1456.828302021-04-16T16:22:00+00:00"Burioni, R."https://www.zbmath.org/authors/?q=ai:burioni.raffaella"Gradenigo, G."https://www.zbmath.org/authors/?q=ai:gradenigo.giacomo"Sarracino, A."https://www.zbmath.org/authors/?q=ai:sarracino.alessandro"Vezzani, A."https://www.zbmath.org/authors/?q=ai:vezzani.alessandro"Vulpiani, A."https://www.zbmath.org/authors/?q=ai:vulpiani.angeloProposal for a conformal field theory interpretation of Watts' differential equation for percolation.https://www.zbmath.org/1456.824602021-04-16T16:22:00+00:00"Flohr, Michael"https://www.zbmath.org/authors/?q=ai:flohr.michael-a-i"Müller-Lohmann, Annekathrin"https://www.zbmath.org/authors/?q=ai:muller-lohmann.annekathrinQuantum Langevin equation.https://www.zbmath.org/1456.602172021-04-16T16:22:00+00:00"de Oliveira, Mário J."https://www.zbmath.org/authors/?q=ai:de-oliveira.mario-jLight scattering as a Poisson process and first-passage probability.https://www.zbmath.org/1456.602722021-04-16T16:22:00+00:00"Zeller, Claude"https://www.zbmath.org/authors/?q=ai:zeller.claude"Cordery, Robert"https://www.zbmath.org/authors/?q=ai:cordery.robertBoolean constraint satisfaction problems for reaction networks.https://www.zbmath.org/1456.827912021-04-16T16:22:00+00:00"Seganti, A."https://www.zbmath.org/authors/?q=ai:seganti.a"De Martino, A."https://www.zbmath.org/authors/?q=ai:martino.a-de|de-martino.antonino|de-martino.alessandro|de-martino.andrea"Ricci-Tersenghi, F."https://www.zbmath.org/authors/?q=ai:ricci-tersenghi.federicoOn the waiting times to repeated hits of cells by particles for the polynomial allocation scheme.https://www.zbmath.org/1456.600352021-04-16T16:22:00+00:00"Selivanov, Boris I."https://www.zbmath.org/authors/?q=ai:selivanov.boris-i"Chistyakov, Vladimir P."https://www.zbmath.org/authors/?q=ai:chistyakov.vladimir-pSummary: We consider random polynomial allocations of particles over \(N\) cells. Let \(\tau_k\), \(k \geq 1\), be the minimal number of trials when \(k\) particles hit the occupied cells. For the case \(N \rightarrow \infty\) the limit distribution of the random variable \(\tau_k/\sqrt{N}\) is found. An example of application of \(\tau_k\) is given.Mean conservation of nodal volume and connectivity measures for Gaussian ensembles.https://www.zbmath.org/1456.824542021-04-16T16:22:00+00:00"Beliaev, Dmitry"https://www.zbmath.org/authors/?q=ai:beliaev.dmitri-b"Muirhead, Stephen"https://www.zbmath.org/authors/?q=ai:muirhead.stephen"Wigman, Igor"https://www.zbmath.org/authors/?q=ai:wigman.igorSummary: We study in depth the nesting graph and volume distribution of the nodal domains of a Gaussian field, which have been shown in previous works to exhibit asymptotic laws. A striking link is established between the asymptotic mean connectivity of a nodal domain (i.e. the vertex degree in its nesting graph) and the positivity of the percolation probability of the field, along with a direct dependence of the average nodal volume on the percolation probability. Our results support the prevailing ansatz that the mean connectivity and volume of a nodal domain is conserved for generic random fields in dimension \(d = 2\) but not in \(d \geq 3\), and are applied to a number of concrete motivating examples.Dynamical robustness of discrete conservative systems: Harper and generalized standard maps.https://www.zbmath.org/1456.601302021-04-16T16:22:00+00:00"Tirnakli, Ugur"https://www.zbmath.org/authors/?q=ai:tirnakli.ugur"Tsallis, Constantino"https://www.zbmath.org/authors/?q=ai:tsallis.constantino"Cetin, Kivanc"https://www.zbmath.org/authors/?q=ai:cetin.kivancMarkov approximations of Gibbs measures for long-range interactions on 1D lattices.https://www.zbmath.org/1456.821532021-04-16T16:22:00+00:00"Maldonado, Cesar"https://www.zbmath.org/authors/?q=ai:maldonado.cesar"Salgado-García, Raúl"https://www.zbmath.org/authors/?q=ai:salgado-garcia.raulExtinction in four species cyclic competition.https://www.zbmath.org/1456.921192021-04-16T16:22:00+00:00"Intoy, Ben"https://www.zbmath.org/authors/?q=ai:intoy.ben"Pleimling, Michel"https://www.zbmath.org/authors/?q=ai:pleimling.michelStability of regime-switching jump diffusion processes.https://www.zbmath.org/1456.602032021-04-16T16:22:00+00:00"Ji, Huijie"https://www.zbmath.org/authors/?q=ai:ji.huijie"Shao, Jinghai"https://www.zbmath.org/authors/?q=ai:shao.jinghai"Xi, Fubao"https://www.zbmath.org/authors/?q=ai:xi.fubaoSummary: This work studies the stability of regime-switching jump diffusion processes in a finite or a countably infinite state space. Some criteria with sufficient conditions for stability and instability are provided based on characterizing the stability property of the processes in any fixed state through constants under common measurements. Also, some variational formula of these constants are given. Moreover, some examples of nonlinear regime-switching jump diffusion processes are provided to show the usefulness and sharpness of these criteria.Modeling interacting dynamic networks. I: Preferred degree networks and their characteristics.https://www.zbmath.org/1456.824162021-04-16T16:22:00+00:00"Liu, Wenjia"https://www.zbmath.org/authors/?q=ai:liu.wenjia"Jolad, Shivakumar"https://www.zbmath.org/authors/?q=ai:jolad.shivakumar"Schmittmann, Beate"https://www.zbmath.org/authors/?q=ai:schmittmann.beate"Zia, R. K. P."https://www.zbmath.org/authors/?q=ai:zia.r-k-pAnomalous diffusion and random search in \textit{xyz}-comb: exact results.https://www.zbmath.org/1456.602772021-04-16T16:22:00+00:00"Lenzi, E. K."https://www.zbmath.org/authors/?q=ai:kaminski-lenzi.ervin"Sandev, T."https://www.zbmath.org/authors/?q=ai:sandev.trifce"Ribeiro, H. V."https://www.zbmath.org/authors/?q=ai:ribeiro.haroldo-v"Jovanovski, P."https://www.zbmath.org/authors/?q=ai:jovanovski.petar"Iomin, A."https://www.zbmath.org/authors/?q=ai:iomin.alexander"Kocarev, L."https://www.zbmath.org/authors/?q=ai:kocarev.ljupcoOn the emergence of an ``intention field'' for socially cohesive agents.https://www.zbmath.org/1456.910912021-04-16T16:22:00+00:00"Bouchaud, Jean-Philippe"https://www.zbmath.org/authors/?q=ai:bouchaud.jean-philippe"Borghesi, Christian"https://www.zbmath.org/authors/?q=ai:borghesi.christian"Jensen, Pablo"https://www.zbmath.org/authors/?q=ai:jensen.pabloThe probability that all eigenvalues are real for products of truncated real orthogonal random matrices.https://www.zbmath.org/1456.150352021-04-16T16:22:00+00:00"Forrester, Peter J."https://www.zbmath.org/authors/?q=ai:forrester.peter-j"Kumar, Santosh"https://www.zbmath.org/authors/?q=ai:kumar.santosh.3|kumar.santosh.4|kumar.santosh.2|kumar.santosh.1Summary: The probability that all eigenvalues of a product of \(m\) independent \(N \times N\) subblocks of a Haar distributed random real orthogonal matrix of size \((L_i+N) \times (L_i+N)\), \((i=1,\dots ,m)\) are real is calculated as a multidimensional integral, and as a determinant. Both involve Meijer G-functions. Evaluation formulae of the latter, based on a recursive scheme, allow it to be proved that for any \(m\) and with each \(L_i\) even the probability is a rational number. The formulae furthermore provide for explicit computation in small order cases.Ergodicity of stochastic differential equations with jumps and singular coefficients.https://www.zbmath.org/1456.601542021-04-16T16:22:00+00:00"Xie, Longjie"https://www.zbmath.org/authors/?q=ai:xie.longjie"Zhang, Xicheng"https://www.zbmath.org/authors/?q=ai:zhang.xichengSummary: We show the strong well-posedness of SDEs driven by general multiplicative Lévy noises with Sobolev diffusion and jump coefficients and integrable drifts. Moreover, we also study the strong Feller property, irreducibility as well as the exponential ergodicity of the corresponding semigroup when the coefficients are time-independent and singular dissipative. In particular, the large jump is allowed in the equation. To achieve our main results, we present a general approach for treating the SDEs with jumps and singular coefficients so that one just needs to focus on Krylov's a priori estimates for SDEs.Stochastic resonance in a non-Poissonian dichotomous process: a new analytical approach.https://www.zbmath.org/1456.600912021-04-16T16:22:00+00:00"Bologna, Mauro"https://www.zbmath.org/authors/?q=ai:bologna.mauro"Chandía, Kristopher J."https://www.zbmath.org/authors/?q=ai:chandia.kristopher-j"Tellini, Bernardo"https://www.zbmath.org/authors/?q=ai:tellini.bernardoGenerally covariant state-dependent diffusion.https://www.zbmath.org/1456.827862021-04-16T16:22:00+00:00"Polettini, Matteo"https://www.zbmath.org/authors/?q=ai:polettini.matteoTotal variation distance between stochastic polynomials and invariance principles.https://www.zbmath.org/1456.600702021-04-16T16:22:00+00:00"Bally, Vlad"https://www.zbmath.org/authors/?q=ai:bally.vlad"Caramellino, Lucia"https://www.zbmath.org/authors/?q=ai:caramellino.luciaSuppose that a sequence \(X=(X_n)_{n \in \mathbb N}\) consists of independent random variables, which have finite moments of any order. This paper considers stochastic polynomials \[Q_{N,k_ *}(c,X) = \sum\limits_{m = 0}^N\Phi _m(c,X),\] where
\[\Phi_m(c,X) := \sum\limits_{k_1,\dots,k_m=1}^{k_ *}\sum\limits_{n_1<\dots <n_m=1}^\infty c((n_1,k_1),\dots,(n_m,k_m)) \times \mathop \Pi \limits_{j = 1}^m (X_{n_j}^{k_j}-\mathrm{E}(X_{n_j}^{k_j})).\] The coefficients \(c\) are symmetric and null on the diagonals and only a finite number of them are nonnull. Here \(X_n\in\mathbb{R}\), but the paper deals with\(X_n\in\mathbb{R}^{d_ *}\). The authors indicate that these multilinear stochastic polynomials are a natural generalization of elements of the classical Wiener chaos. In addition, they are of interest in applications to \(U\)-statistics theory. The goal of the paper is to estimate the total variation distance between the laws of two such polynomials, and to establish an invariance principle.
Reviewer: Oleg K. Zakusilo (Kyïv)Edgeworth corrections for spot volatility estimator.https://www.zbmath.org/1456.622472021-04-16T16:22:00+00:00"He, Lidan"https://www.zbmath.org/authors/?q=ai:he.lidan"Liu, Qiang"https://www.zbmath.org/authors/?q=ai:liu.qiang"Liu, Zhi"https://www.zbmath.org/authors/?q=ai:liu.zhiSummary: We develop Edgeworth expansion theory for spot volatility estimator under general assumptions on the log-price process that allow for drift and leverage effect. The result is based on further estimation of skewness and kurtosis, when compared with existing second order asymptotic normality result. Thus our theory can provide with a refinement result for the finite sample distribution of spot volatility. We also construct feasible confidence intervals (one-sided and two-sided) for spot volatility by using Edgeworth expansion. The Monte Carlo simulation study we conduct shows that the intervals based on Edgeworth expansion perform better than the conventional intervals based on normal approximation, which justifies the correctness of our theoretical conclusion.On the formation of structure in growing networks.https://www.zbmath.org/1456.900352021-04-16T16:22:00+00:00"Moriano, P."https://www.zbmath.org/authors/?q=ai:moriano.p"Finke, J."https://www.zbmath.org/authors/?q=ai:finke.juergen|finke.jorgeLarge deviations of generalized renewal process.https://www.zbmath.org/1456.602332021-04-16T16:22:00+00:00"Bakay, Gavriil A."https://www.zbmath.org/authors/?q=ai:bakay.gavriil-a"Shklyaev, Aleksandr V."https://www.zbmath.org/authors/?q=ai:shklyaev.aleksandr-vSummary: Let \((\xi(i), \eta (i)) \in \mathbb{R}^{d+1}\), \(1 \leq i < \infty \), be independent identically distributed random vectors, \( \eta (i)\) be nonnegative random variables, the vector \(( \xi(1), \eta (1))\) satisfy the Cramer condition. On the base of renewal process, \(N_T = \max\{ k : \eta (1) + \dots + \eta (k) \leq T\}\) we define the generalized renewal process \(Z_T = \sum_{i=1}^{N_T} \xi (i)\). Put \(I_{ \Delta_T}(x) = \{ y \in \mathbb{R}^d : x_j \leq y_j < x_j + \Delta_T , j = 1, \dots, d\}\). We find asymptotic formulas for the probabilities \(\mathbf{P}(Z_T \in I_{ \Delta_T }(x))\) as \(\Delta_T \rightarrow 0\) and \(\mathbf{P}( Z_T = x)\) in non-lattice and arithmetic cases, respectively, in a wide range of \(x\) values, including normal, moderate, and large deviations. The analogous results were obtained for a process with delay in which the distribution of \(( \xi(1), \eta (1))\) differs from the distribution on the other steps. Using these results, we prove local limit theorems for processes with regeneration and for additive functionals of finite Markov chains, including normal, moderate, and large deviations.Determination of \(S\)-curves with applications to the theory of non-Hermitian orthogonal polynomials.https://www.zbmath.org/1456.823362021-04-16T16:22:00+00:00"Álvarez, Gabriel"https://www.zbmath.org/authors/?q=ai:alvarez.gabriel"Martínez Alonso, Luis"https://www.zbmath.org/authors/?q=ai:martinez-alonso.luis"Medina, Elena"https://www.zbmath.org/authors/?q=ai:medina.elenaStructural equation modeling. Applications using Mplus. 2nd edition.https://www.zbmath.org/1456.620092021-04-16T16:22:00+00:00"Wang, Jichuan"https://www.zbmath.org/authors/?q=ai:wang.jichuan"Wang, Xiaoqian"https://www.zbmath.org/authors/?q=ai:wang.xiaoqianPublisher's description: Focusing on the conceptual and practical aspects of Structural Equation Modeling (SEM), this book demonstrates basic concepts and examples of various SEM models, along with updates on many advanced methods, including confirmatory factor analysis (CFA) with categorical items, bifactor model, Bayesian CFA model, item response theory (IRT) model, graded response model (GRM), multiple imputation (MI) of missing values, plausible values of latent variables, moderated mediation model, Bayesian SEM, latent growth modeling (LGM) with individually varying times of observations, dynamic structural equation modeling (DSEM), residual dynamic structural equation modeling (RDSEM), testing measurement invariance of instrument with categorical variables, longitudinal latent class analysis (LLCA), latent transition analysis (LTA), growth mixture modeling (GMM) with covariates and distal outcome, manual implementation of the BCH method and the three-step method for mixture modeling, Monte Carlo simulation power analysis for various SEM models, and estimate sample size for latent class analysis (LCA) model.
The statistical modeling program Mplus Version 8.2 is featured with all models updated. It provides researchers with a flexible tool that allows them to analyze data with an easy-to-use interface and graphical displays of data and analysis results.
Intended as both a teaching resource and a reference guide, and written in non-mathematical terms, Structural Equation Modeling: Applications Using Mplus, 2nd edition provides step-by-step instructions of model specification, estimation, evaluation, and modification. Chapters cover: Confirmatory Factor Analysis (CFA); Structural Equation Models (SEM); SEM for Longitudinal Data; Multi-Group Models; Mixture Models; and Power Analysis and Sample Size Estimate for SEM.
\begin {itemize}
\item Presents a useful reference guide for applications of SEM while systematically demonstrating various advanced SEM models
\item Discusses and demonstrates various SEM models using both cross-sectional and longitudinal data with both continuous and categorical outcomes
\item Provides step-by-step instructions of model specification and estimation, as well as detailed interpretation of Mplus results using real data sets
\item Introduces different methods for sample size estimate and statistical power analysis for SEM
\end {itemize}
Structural Equation Modeling is an excellent book for researchers and graduate students of SEM who want to understand the theory and learn how to build their own SEM models using Mplus.On the work distribution in quasi-static processes.https://www.zbmath.org/1456.825592021-04-16T16:22:00+00:00"Hoppenau, Johannes"https://www.zbmath.org/authors/?q=ai:hoppenau.johannes"Engel, Andreas"https://www.zbmath.org/authors/?q=ai:engel.andreas-k|engel.andreasOn the optimality of the aggregate with exponential weights for low temperatures.https://www.zbmath.org/1456.621362021-04-16T16:22:00+00:00"Lecué, Guillaume"https://www.zbmath.org/authors/?q=ai:lecue.guillaume"Mendelson, Shahar"https://www.zbmath.org/authors/?q=ai:mendelson.shahar(no abstract)Existence of densities for the dynamic \(\Phi^4_3\) model.https://www.zbmath.org/1456.601372021-04-16T16:22:00+00:00"Gassiat, Paul"https://www.zbmath.org/authors/?q=ai:gassiat.paul"Labbé, Cyril"https://www.zbmath.org/authors/?q=ai:labbe.cyrilSummary: We apply Malliavin calculus to the \(\Phi^4_3\) equation on the torus and prove existence of densities for the solution of the equation evaluated at regular enough test functions. We work in the framework of regularity structures and rely on Besov-type spaces of modelled distributions in order to prove Malliavin differentiability of the solution. Our result applies to a large family of Gaussian space-time noises including white noise, in particular the noise may be degenerate as long as it is sufficiently rough on small scales.On laws of large numbers in \(L^2\) for supercritical branching Markov processes beyond \(\lambda \)-positivity.https://www.zbmath.org/1456.600732021-04-16T16:22:00+00:00"Jonckheere, Matthieu"https://www.zbmath.org/authors/?q=ai:jonckheere.matthieu"Saglietti, Santiago"https://www.zbmath.org/authors/?q=ai:saglietti.santiagoThe processes considered are supercritical Markov branching processes \((\xi_t)_{t\ge 0}\) with a general type space \((J,\mathcal{B}_J)\), a constant, i.e., type-independent branching rate, a constant local branching law with finite second moment and with possible absorbing states on \(\overline{J}\backslash J\). The aim is to provide conditions, covering as many different examples as possible, for \(L^2\)-convergence, as \(t\to\infty\), of \(\xi_t(B)/\mathbf{E}\,\xi_t(B')\) to \(\nu(B)D_\infty/\nu(B')\), where \(\xi_t(B)\) is the number of particles in \(B\) at time \(t\), \(\nu\) a measure on \((J,\mathcal{B}_J)\), \(D_\infty\) a nonnegative random variable and \(B\), \(B'\) are sets in some class \(\mathcal{C}\subseteq \mathcal{B}_J\), \(\nu(B')\ne 0\). Proceeding probabilistically and using spatial decomposition techniques, it is shown that whenever the distribution of the ``immortal particle'' process is regularly varying, as \(t\to\infty\), \(L^2\)-convergence holds if and only if a specific additive martingale associated with the branching process is bounded in \(L^2\). Given that boundedness, \(D_\infty\) is the \(L^2\)-limit of the martingale. An explicit formula for the asymptotic variance of the martingale is obtained, so that boundedness can be checked by direct computation. Conditions for \(\mathbf{P}(D_\infty> 0\mid\text{survival})=1\) are investigated and several examples discussed, among them classical \(\lambda\)-positive processes and, in particular, the non-\(\lambda\)-positive branching Brownian motion with drift and absorption at 0 introduced by \textit{H. Kesten} [Stochastic Processes Appl. 7, 9--47 (1978; Zbl 0383.60077)].
Reviewer: Heinrich Hering (Rockenberg)Estimation of the lead-lag parameter from non-synchronous data.https://www.zbmath.org/1456.622482021-04-16T16:22:00+00:00"Hoffmann, M."https://www.zbmath.org/authors/?q=ai:hoffmann.marc-r"Rosenbaum, M."https://www.zbmath.org/authors/?q=ai:rosenbaum.mathieu"Yoshida, N."https://www.zbmath.org/authors/?q=ai:yoshida.nozomu|yoshida.norio|yoshida.naoki|yoshida.naoshi|yoshida.norimasa|yoshida.noriyoshi|yoshida.naohiro|yoshida.nakahiro|yoshida.naofumi|yoshida.natsumi|yoshida.noriaki|yoshida.norinobu|yoshida.nobuyuki|yoshida.naoya|yoshida.naoto|yoshida.nobuakiSummary: We propose a simple continuous time model for modeling the lead-lag effect between two financial assets. A two-dimensional process \((X_{t},Y_{t})\) reproduces a lead-lag effect if, for some time shift \(\vartheta \in \mathbb{R} \), the process \((X_{t},Y_{t+\vartheta})\) is a semi-martingale with respect to a certain filtration. The value of the time shift \(\vartheta\) is the lead-lag parameter. Depending on the underlying filtration, the standard no-arbitrage case is obtained for \(\vartheta=0\). We study the problem of estimating the unknown parameter \(\vartheta \in \mathbb{R}\), given randomly sampled non-synchronous data from \((X_{t})\) and \((Y_{t})\). By applying a certain contrast optimization based on a modified version of the Hayashi-Yoshida covariation estimator, we obtain a consistent estimator of the lead-lag parameter, together with an explicit rate of convergence governed by the sparsity of the sampling design.Statistical inference for discrete-time samples from affine stochastic delay differential equations.https://www.zbmath.org/1456.620352021-04-16T16:22:00+00:00"Küchler, Uwe"https://www.zbmath.org/authors/?q=ai:kuechler.uwe"Sørensen, Michael"https://www.zbmath.org/authors/?q=ai:sorensen.michaelSummary: Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class of prediction-based estimating functions is investigated as well. In particular, the optimal prediction-based estimating function and the asymptotic properties of the estimators are derived. The maximum pseudo-likelihood estimator is a particular case, and an expression is found for the efficiency loss when using the maximum pseudo-likelihood estimator, rather than the computationally more involved optimal prediction-based estimator. The distribution of the pseudo-likelihood estimator is investigated in a simulation study. Two examples of affine stochastic delay equation are considered in detail.Space-fractional Fokker-Planck equation and optimization of random search processes in the presence of an external bias.https://www.zbmath.org/1456.827842021-04-16T16:22:00+00:00"Palyulin, Vladimir V."https://www.zbmath.org/authors/?q=ai:palyulin.vladimir-v"Chechkin, Aleksei V."https://www.zbmath.org/authors/?q=ai:chechkin.aleksei-v"Metzler, Ralf"https://www.zbmath.org/authors/?q=ai:metzler.ralfFull counting statistics and the Edgeworth series for matrix product states.https://www.zbmath.org/1456.821872021-04-16T16:22:00+00:00"Shi, Yifei"https://www.zbmath.org/authors/?q=ai:shi.yifei"Klich, Israel"https://www.zbmath.org/authors/?q=ai:klich.israelAn order approach to SPDEs with antimonotone terms.https://www.zbmath.org/1456.352452021-04-16T16:22:00+00:00"Scarpa, Luca"https://www.zbmath.org/authors/?q=ai:scarpa.luca"Stefanelli, Ulisse"https://www.zbmath.org/authors/?q=ai:stefanelli.ulisseSummary: We consider a class of parabolic stochastic partial differential equations featuring an antimonotone nonlinearity. The existence of unique maximal and minimal variational solutions is proved via a fixed-point argument for nondecreasing mappings in ordered spaces. This relies on the validity of a comparison principle.Transitions of generalised Bessel kernels related to biorthogonal ensembles.https://www.zbmath.org/1456.150372021-04-16T16:22:00+00:00"Kawamoto, Yosuke"https://www.zbmath.org/authors/?q=ai:kawamoto.yosukeSummary: Biorthogonal ensembles are generalisations of classical orthogonal ensembles such as the Laguerre or the Hermite ensembles. Local fluctuation of these ensembles at the origin has been studied, and determinantal kernels in the limit are described by the Wright generalised Bessel functions. The limit kernels are one parameter deformations of the Bessel kernel and the sine kernel for the Laguerre weight and the Hermite weight, respectively. We study transitions from these generalised Bessel kernels to the sine kernel under appropriate scaling limits in common with classical kernels.Support theorem for an SPDE with multiplicative noise driven by a cylindrical Wiener process on the real line.https://www.zbmath.org/1456.352472021-04-16T16:22:00+00:00"Yastrzhembskiy, Timur"https://www.zbmath.org/authors/?q=ai:yastrzhembskiy.timurSummary: We prove a Stroock-Varadhan's type support theorem for a stochastic partial differential equation on the real line with a noise term driven by a cylindrical Wiener process on \(L_2 (\mathbb{R})\). The main ingredients of the proof are V. Mackevičius's approach to support theorem for diffusion processes and N.V. Krylov's \(L_p\)-theory of SPDEs.On the density of the supremum of the solution to the linear stochastic heat equation.https://www.zbmath.org/1456.601582021-04-16T16:22:00+00:00"Dalang, Robert C."https://www.zbmath.org/authors/?q=ai:dalang.robert-c"Pu, Fei"https://www.zbmath.org/authors/?q=ai:pu.feiThe authors are interested in the existence and properties of the probability density function of the supremum
of the solutions to SPDEs (stochastic partial differential equations). This is partly motivated by the fact that the density of the supremum of the solution is related to the study of upper bounds on hitting
probabilities for these solutions. They consider the linear stochastic heat equation with zero initial condition, either Neumann or Dirichlet boundary conditions, and Brownian sheet on \([0,\infty)\times[0,1]\) as the random noise. The mild solution is defined via the Green kernel. The goal of the paper is to establish the smoothness
of the joint density of the random vector whose components are the solution and the
supremum of an increment in time of the solution over an interval (at a fixed spatial
position), and the smoothness of the density of the supremum of the solution over
a space-time rectangle that touches the \(t = 0\) axis, using a general criterion for the smoothness
of densities for locally nondegenerate random variables. Applying the Malliavin calculus, in particular, Malliavin derivatives and properties of the
divergence operator, the authors establish a Gaussian-type upper bound on these two densities
respectively, which presents a close connection with the Hölder-continuity properties
of the solution.
Reviewer: Yuliya S. Mishura (Kyïv)Constrained total undiscounted continuous-time Markov decision processes.https://www.zbmath.org/1456.901732021-04-16T16:22:00+00:00"Guo, Xianping"https://www.zbmath.org/authors/?q=ai:guo.xianping"Zhang, Yi"https://www.zbmath.org/authors/?q=ai:zhang.yi.2Summary: The present paper considers the constrained optimal control problem with total undiscounted criteria for a continuous-time Markov decision process (CTMDP) in Borel state and action spaces. The cost rates are nonnegative. Under the standard compactness and continuity conditions, we show the existence of an optimal stationary policy out of the class of general nonstationary ones. In the process, we justify the reduction of the CTMDP model to a discrete-time Markov decision process (DTMDP) model based on the studies of the undiscounted occupancy and occupation measures. We allow that the controlled process is not necessarily absorbing, and the transition rates are not necessarily separated from zero, and can be arbitrarily unbounded; these features count for the main technical difficulties in studying undiscounted CTMDP models.Hardy's function \(Z(t)\): results and problems.https://www.zbmath.org/1456.111602021-04-16T16:22:00+00:00"Ivić, Aleksandar"https://www.zbmath.org/authors/?q=ai:ivic.aleksandarSummary: This is primarily an overview article on some results and problems involving the classical Hardy function \(Z(t):= \zeta(1/2 + it)(\chi(1/2 + it))^{-1/2}\), \(\zeta(s) = \chi(s)\zeta(1-s)\). In particular, we discuss the first and third moments of \(Z(t)\) (with and without shifts) and the distribution of its positive and negative values. A new result involving the distribution of its values is presented.Double roots of random Littlewood polynomials.https://www.zbmath.org/1456.601292021-04-16T16:22:00+00:00"Peled, Ron"https://www.zbmath.org/authors/?q=ai:peled.ron"Sen, Arnab"https://www.zbmath.org/authors/?q=ai:sen.arnab"Zeitouni, Ofer"https://www.zbmath.org/authors/?q=ai:zeitouni.oferSummary: We consider random polynomials whose coefficients are independent and uniform on \(\{-1,1\}\). We prove that the probability that such a polynomial of degree \(n\) has a double root is \(o(n^{-2})\) when \(n+1\) is not divisible by 4 and asymptotic to \(\frac{8\sqrt 3}{\pi n^2}\) otherwise. This result is a corollary of a more general theorem that we prove concerning random polynomials with independent, identically distributed coefficients having a distribution which is supported on \(\{-1,0,1\}\) and whose largest atom is strictly less than \(1/\sqrt 3\). In this general case, we prove that the probability of having a double root equals the probability that either \(-1\), \(0\) or \(1\) are double roots up to an \(o(n^{-2})\) factor and we find the asymptotics of the latter probability.Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient.https://www.zbmath.org/1456.602052021-04-16T16:22:00+00:00"Boyer, Denis"https://www.zbmath.org/authors/?q=ai:boyer.denis"Dean, David S."https://www.zbmath.org/authors/?q=ai:dean.david-s"Mejía-Monasterio, Carlos"https://www.zbmath.org/authors/?q=ai:mejia-monasterio.carlos"Oshanin, Gleb"https://www.zbmath.org/authors/?q=ai:oshanin.glebNon universality of fluctuations of outlier eigenvectors for block diagonal deformations of Wigner matrices.https://www.zbmath.org/1456.150332021-04-16T16:22:00+00:00"Capitaine, Mireille"https://www.zbmath.org/authors/?q=ai:capitaine.mireille"Donati-Martin, Catherine"https://www.zbmath.org/authors/?q=ai:donati-martin.catherineSummary: In this paper, we investigate the fluctuations of a unit eigenvector associated to an outlier in the spectrum of a spiked \(N \times N\) complex Deformed Wigner matrix \(M_N\). \(M_N\) is defined as follows: \(M_N=W_N/\sqrt{N}+A_N\) where \(W_N\) is an \(N \times N\) Hermitian Wigner matrix whose entries have a law \(\mu\) satisfying a Poincaré inequality and the matrix \(A_N\) is a block diagonal matrix, with an eigenvalue \(\theta\) of multiplicity one, generating an outlier in the spectrum of \(M_N\). We prove that the fluctuations of the norm of the projection of a unit eigenvector corresponding to the outlier of \(M_N\) onto a unit eigenvector corresponding to \(\theta\) are not universal. Indeed, we take away a fit approximation of its limit from this norm and prove the convergence to zero as \(N\) goes to \(\infty\) of the Lévy-Prohorov distance between this rescaled quantity and the convolution of \(\mu\) and a centered Gaussian distribution (whose variance may depend depend upon \(N\) and may not converge).Continuity of zero-hitting times of Bessel processes and welding homeomorphisms of \(\operatorname{SLE}_k\).https://www.zbmath.org/1456.300392021-04-16T16:22:00+00:00"Beliaev, Dmitry"https://www.zbmath.org/authors/?q=ai:beliaev.dmitri-b"Margarint, Vlad"https://www.zbmath.org/authors/?q=ai:margarint.vlad"Shekhar, Atul"https://www.zbmath.org/authors/?q=ai:shekhar.atulSummary: We consider a family of Bessel Processes that depend on the starting point \(x\) and dimension \(\delta\), but are driven by the same Brownian motion. Our main result is that almost surely the first time a process hits 0 is jointly continuous in \(x\) and \(\delta\), provided \(\delta \leq 0\). As an application, we show that the \(\operatorname{SLE}(\kappa)\) welding homeomorphism is continuous in \(\kappa\) for \(\kappa \in [0,4]\). Our motivation behind this is to study the well known problem of the continuity of \(\operatorname{SLE} \kappa\) in \(\kappa\). The main tool in our proofs is random walks with increments distributed as infinite mean Inverse-Gamma laws.General contact process with rapid stirring.https://www.zbmath.org/1456.826842021-04-16T16:22:00+00:00"Mytnik, Leonid"https://www.zbmath.org/authors/?q=ai:mytnik.leonid"Shlomov, Segev"https://www.zbmath.org/authors/?q=ai:shlomov.segevSummary: We study the limiting behavior of an interacting particle system evolving on the lattice \(\mathbb{Z}^d\) for \(d \geq 3\). The model is known as the contact process with rapid stirring. The process starts with a single particle at the origin. Each particle may die, jump to a neighboring site if it is vacant or split. In the case of splitting, one of the offspring takes the place of the parent while the other, the newborn particle, is sent to another site in \(\mathbb{Z}^d\) according to a certain distribution; if the newborn particle lands on an occupied site, its birth is suppressed. We study the asymptotic behavior of the critical branching rate as the jumping rate (also known as the stirring rate) approaches infinity.Average harmonic spectrum of the whole-plane SLE.https://www.zbmath.org/1456.827762021-04-16T16:22:00+00:00"Loutsenko, Igor"https://www.zbmath.org/authors/?q=ai:loutsenko.igor-m"Yermolayeva, Oksana"https://www.zbmath.org/authors/?q=ai:yermolayeva.oksanaStopping with expectation constraints: 3 points suffice.https://www.zbmath.org/1456.600942021-04-16T16:22:00+00:00"Ankirchner, Stefan"https://www.zbmath.org/authors/?q=ai:ankirchner.stefan"Kazi-Tani, Nabil"https://www.zbmath.org/authors/?q=ai:kazi-tani.nabil"Klein, Maike"https://www.zbmath.org/authors/?q=ai:klein.maike"Kruse, Thomas"https://www.zbmath.org/authors/?q=ai:kruse.thomasThe paper deals with a problem of optimally stopping a process with a stopping time satisfying an expectation constraint. Let \((Y_t)_{t\in\Re^+}\) be a one-dimensional regular continuous strong Markov process with respect to a right-continuous filtration \((\mathcal{F}_t)\). The state space \(J\subset\Re\) is assumed to be an open, half-open or closed interval. The payoff \(f : \Re\rightarrow\Re\) is a Borel-measurable having regularity conditions. Let us denote by \(\mathcal{T} (\mathbf{T})\) the set of \((\mathcal{F}_t)\)-stopping times such that \(\mathbf{E}[\tau]\leq \mathbf{T}\in \Re^+\). The problem considered in the paper has the form: \(\max_{\tau\in \mathcal{T} (\mathbf{T})} \textbf{E}[f(Y_\tau)]\).
It is shown that to obtain a solution of such constrained optimization problem it suffices to consider only stopping times such that the law of the process at the stopping time is a weighted sum of 3 Dirac measures. The idea for proving a reduction to 3 Dirac measures is based on rewriting the considered constrained stopping problem as a linear optimization problem over a set of probability measures. Recent results of \textit{S. Ankirchner} et al. [Bernoulli 21, No. 2, 1067--1088 (2015; Zbl 1328.60101)] and \textit{D. Hobson} [Electron. J. Probab. 20, Paper No. 83, 26 p. (2015; Zbl 1328.60104)] on the Skorokhod embedding problem characterizing the set \(\mathcal{A}(\mathbf{T})\) of probability distributions that can be embedded into \(Y\) with stopping times having expectation smaller than or equal to \(\mathbf{T}\). As for standard linear problems the maximal value of the optimization is attained by extreme points. The extreme points of \(\mathcal{A}(\mathbf{T})\) turn out to be contained in the set of probability measures that can be written as weighted sums of at most 3 Dirac measures.
Reviewer: Krzysztof J. Szajowski (Wrocław)Stein's method for normal approximation in Wasserstein distances with application to the multivariate central limit theorem.https://www.zbmath.org/1456.600592021-04-16T16:22:00+00:00"Bonis, Thomas"https://www.zbmath.org/authors/?q=ai:bonis.thomasSummary: We use Stein's method to bound the Wasserstein distance of order 2 between a measure \(\nu\) and the Gaussian measure using a stochastic process \((X_t)_{t \ge 0}\) such that \(X_t\) is drawn from \(\nu\) for any \(t > 0\). If the stochastic process \((X_t)_{t \ge 0}\) satisfies an additional exchangeability assumption, we show it can also be used to obtain bounds on Wasserstein distances of any order \(p \ge 1\). Using our results, we provide convergence rates for the multi-dimensional central limit theorem in terms of Wasserstein distances of any order \(p \ge 2\) under simple moment assumptions.Passage-time coding with a timing kernel inferred from irregular cortical spike sequences.https://www.zbmath.org/1456.920362021-04-16T16:22:00+00:00"Tsubo, Yasuhiro"https://www.zbmath.org/authors/?q=ai:tsubo.yasuhiro"Isomura, Yoshikazu"https://www.zbmath.org/authors/?q=ai:isomura.yoshikazu"Fukai, Tomoki"https://www.zbmath.org/authors/?q=ai:fukai.tomokiBeyond mean field theory: statistical field theory for neural networks.https://www.zbmath.org/1456.824082021-04-16T16:22:00+00:00"Buice, Michael A."https://www.zbmath.org/authors/?q=ai:buice.michael-a"Chow, Carson C."https://www.zbmath.org/authors/?q=ai:chow.carson-cOscillation properties of expected stopping times and stopping probabilities for patterns consisting of consecutive states in Markov chains.https://www.zbmath.org/1456.601792021-04-16T16:22:00+00:00"Kerimov, Azer"https://www.zbmath.org/authors/?q=ai:kerimov.a-a"Öner, Abdullah"https://www.zbmath.org/authors/?q=ai:oner.abdullahSummary: We investigate a Markov chain with a state space \(1, 2, \ldots, r\) stopping at appearance of patterns consisting of two consecutive states. It is observed that the expected stopping times of the chain have surprising oscillating dependencies on starting positions. Analogously, the stopping probabilities also have oscillating dependencies on terminal states. In a nonstopping Markov chain the frequencies of appearances of two consecutive states are found explicitly.Absolute negative mobility induced by white Poissonian noise.https://www.zbmath.org/1456.827942021-04-16T16:22:00+00:00"Spiechowicz, J."https://www.zbmath.org/authors/?q=ai:spiechowicz.jakub"Łuczka, J."https://www.zbmath.org/authors/?q=ai:luczka.jerzy"Hänggi, P."https://www.zbmath.org/authors/?q=ai:hanggi.peterLinear fractional stable motion: A wavelet estimator of the \(\alpha\) parameter.https://www.zbmath.org/1456.621772021-04-16T16:22:00+00:00"Ayache, Antoine"https://www.zbmath.org/authors/?q=ai:ayache.antoine"Hamonier, Julien"https://www.zbmath.org/authors/?q=ai:hamonier.julienSummary: Linear fractional stable motion, denoted by \(\{X_{H,\alpha }(t)\}_{t\in \mathbb R}\), is one of the most classical stable processes; it depends on two parameters H\(\in \)(0,1) and \(\alpha \in \)(0,2). The parameter H characterizes the self-similarity property of \(\{X_{H,\alpha }(t)\}_{t\in \mathbb R}\) while the parameter \(\alpha \) governs the tail heaviness of its finite dimensional distributions; throughout our article we assume that the latter distributions are symmetric, that \(H>1/\alpha\) and that H is known. We show that, on the interval [0,1], the asymptotic behavior of the maximum, at a given scale j, of absolute values of the wavelet coefficients of \(\{X_{H,\alpha }(t)\}_{t\in \mathbb R}\), is of the same order as \(2^{ - j(H - 1/\alpha )}\); then we derive from this result a strongly consistent (i.e. almost surely convergent) statistical estimator for the parameter \(\alpha \).Limit theorems for process-level Betti numbers for sparse and critical regimes.https://www.zbmath.org/1456.600442021-04-16T16:22:00+00:00"Owada, Takashi"https://www.zbmath.org/authors/?q=ai:owada.takashi"Thomas, Andrew M."https://www.zbmath.org/authors/?q=ai:thomas.andrew-mA (random) simplicial complex \(\check{C} (\mathcal{X}, t)\), \( t \geq 0\), on a (random) point set \(\mathcal{X} \subset \mathbb{R}^d\) is constructed such that (i) the \(0\)-simplices are the points of \(\mathcal{X}\); (ii) the \(k\)-simplices \([x_0, \ldots, x_k]\) are included if every pair of points in \(\{ x_0, \ldots, x_k \} \subset \mathcal{X}\) lie within distance \(t\).
The probabilistic model is to take \(\mathcal{X} = \mathcal{P}_n\), a Poisson point process of intensity \(n \mu\), where \(\mu\) is a measure on \(\mathbb{R}^d\) with a bounded and continuous density, and to consider topological statistics
of the process \( ( \check{C} ( \mathcal{P}_n , s_n t ) )_{t \geq 0}\) as \(n \to \infty\) for appropriate scaling sequences \(s_n\). In particular, the subject of the present paper is the \(k\)th Betti number process given by \(\beta_{k,n} (t) = \beta_k ( \check{C} ( \mathcal{P}_n , s_n t ) )\). Motivation arises in part from the recent interest in \emph{persistent homology} and topological data analysis.
As in the classical case of the random geometric graph [\textit{M. Penrose}, Random geometric graphs. Oxford: Oxford University Press (2003; Zbl 1029.60007)], the asymptotic behaviour is different in the three regimes \(ns_n^d \to 0\) (sparse), \(n s_n^d \to \infty\) (dense), and \(n s_n^d \to \lambda \in (0,\infty)\) (critical).
The authors first consider the sparse regime where \(n s_n^d \to 0\) but \(n^{k+2} s_n^{d(k+1)} \to \infty\), and show that
\(\beta_{k,n}\) converges in finite-dimensional distributions to a Gaussian process associated with connected components on \(k+2\) points. In an ultra-sparse regime where \(n s_n^d \to 0\) very fast, there is instead a Poisson limit theorem.
In the critical regime with \(s_n = n^{-1/d}\), there is also convergence to a Gaussian limit, but now with a much more complicated structure: it is an infinite sum of Gaussian processes that are associated with components on \(k+2, k+3, \ldots\) points.
Proofs make use of local dependence, Stein's method, and Poisson process technology. The process-versions of these results are new, although marginal central limit theorems were known in some cases: e.g., [\textit{R. Iwasa}, Homology Homotopy Appl. 22, No. 1, 343--374 (2020; Zbl 1435.13013)].
Reviewer: Andrew Wade (Durham)Efficient exponential timestepping algorithm using control variate technique for simulating a functional of exit time of one-dimensional Brownian diffusion with applications in finance.https://www.zbmath.org/1456.601722021-04-16T16:22:00+00:00"Alzubaidi, Hasan"https://www.zbmath.org/authors/?q=ai:alzubaidi.hasanSummary: The exponential timestepping Euler algorithm with a boundary test is adapted to simulate an expected of a function of exit time, such as the expected payoff of barrier options under the constant elasticity of variance (CEV) model. However, this method suffers from a high Monte Carlo (MC) statistical error due to its exponentially large exit times with unbounded samples. To reduce this kind of error efficiently and to speed up the MC simulation, we combine such an algorithm with an effective variance reduction technique called the control variate method. We call the resulting algorithm the improved Exp algorithm for abbreviation. In regard to the examples we consider in this paper for the restricted CEV process, we found that the variance of the improved Exp algorithm is about six times smaller than that of the \textit{K. M. Jansons} and \textit{G. D. Lythe} [J. Stat. Phys. 100, No. 5--6, 1097--1109 (2000; Zbl 0969.65004)] original method for the down-and-out call barrier option. It is also about eight times smaller for the up-and-out put barrier option, indicating that the gain in efficiency is significant without significant increase in simulation time.Fluctuations in quantum one-dimensional thermostatted systems with off-diagonal disorder.https://www.zbmath.org/1456.825802021-04-16T16:22:00+00:00"Colangeli, Matteo"https://www.zbmath.org/authors/?q=ai:colangeli.matteo"Rondoni, Lamberto"https://www.zbmath.org/authors/?q=ai:rondoni.lamberto\(L^p (p > 1)\) solutions of BSDEs with generators satisfying some non-uniform conditions in \(t\) and \(\omega\).https://www.zbmath.org/1456.601512021-04-16T16:22:00+00:00"Liu, Yajun"https://www.zbmath.org/authors/?q=ai:liu.yajun"Li, Depeng"https://www.zbmath.org/authors/?q=ai:li.depeng"Fan, Shengjun"https://www.zbmath.org/authors/?q=ai:fan.shengjunSummary: This paper is devoted to the \(L^p (p > 1)\) solutions of one-dimensional backward stochastic differential equations (BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in \(t\) and \(\omega\). An existence and uniqueness result, a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of \(L^p (p > 1)\) solutions of BSDEs with Lipschitz or linear-growth generators are also developed in this paper.Understanding human dynamics in microblog posting activities.https://www.zbmath.org/1456.910802021-04-16T16:22:00+00:00"Jiang, Zhihong"https://www.zbmath.org/authors/?q=ai:jiang.zhihong"Zhang, Yubao"https://www.zbmath.org/authors/?q=ai:zhang.yubao"Wang, Hui"https://www.zbmath.org/authors/?q=ai:wang.hui.6"Li, Pei"https://www.zbmath.org/authors/?q=ai:li.peiAnalytic subordination theory of operator-valued free additive convolution and the solution of a general random matrix problem.https://www.zbmath.org/1456.600132021-04-16T16:22:00+00:00"Belinschi, Serban T."https://www.zbmath.org/authors/?q=ai:belinschi.serban-teodor"Mai, Tobias"https://www.zbmath.org/authors/?q=ai:mai.tobias"Speicher, Roland"https://www.zbmath.org/authors/?q=ai:speicher.rolandSummary: We develop an analytic theory of operator-valued additive free convolution in terms of subordination functions. In contrast to earlier investigations our functions are not just given by power series expansions, but are defined as Fréchet analytic functions in all of the operator upper half plane. Furthermore, we do not have to assume that our state is tracial. Combining this new analytic theory of operator-valued free convolution with Anderson's selfadjoint version of the linearization trick we are able to provide a solution to the following general random matrix problem: Let \(X_1^{(N)},\dots,X_n^{(N)}\) be selfadjoint \(N\times N\) random matrices which are, for \(N\), asymptotically free. Consider a selfadjoint polynomial \(p\) in \(n\) non-commuting variables and let \(P^{(N)}\) be the element \(P^{(N)}=p(X_1^{(N)},\dots,X_n^{(N)})\). How can we calculate the asymptotic eigenvalue distribution of \(P^{(N)}\) out of the asymptotic eigenvalue distributions of \(X_1^{(N)},\dots,X_n^{(N)}\)?Universality in \(p\)-spin glasses with correlated disorder.https://www.zbmath.org/1456.829062021-04-16T16:22:00+00:00"Bonzom, Valentin"https://www.zbmath.org/authors/?q=ai:bonzom.valentin"Gurau, Razvan"https://www.zbmath.org/authors/?q=ai:gurau.razvan"Smerlak, Matteo"https://www.zbmath.org/authors/?q=ai:smerlak.matteoA local stable bootstrap for power variations of pure-jump semimartingales and activity index estimation.https://www.zbmath.org/1456.621712021-04-16T16:22:00+00:00"Hounyo, Ulrich"https://www.zbmath.org/authors/?q=ai:hounyo.ulrich"Varneskov, Rasmus T."https://www.zbmath.org/authors/?q=ai:varneskov.rasmus-tSummary: We provide a new resampling procedure-the local stable bootstrap-that is able to mimic the dependence properties of realized power variations for pure-jump semimartingales observed at different frequencies. This allows us to propose a bootstrap estimator and inference procedure for the activity index of the underlying process, \(\beta\), as well as bootstrap tests for whether it obeys a jump-diffusion or a pure-jump process, that is, of the null hypothesis \(\mathcal{H}_0:\beta=2\) against the alternative \(\mathcal{H}_1:\beta<2\). We establish first-order asymptotic validity of the resulting bootstrap power variations, activity index estimator, and diffusion tests for \(\mathcal{H}_0\). Moreover, the finite sample size and power properties of the proposed diffusion tests are compared to those of benchmark tests using Monte Carlo simulations. Unlike existing procedures, our bootstrap tests are correctly sized in general settings. Finally, we illustrate the use and properties of the new bootstrap diffusion tests using high-frequency data on three FX series, the S\&P 500, and the VIX.On the spatial persistence for Airy processes.https://www.zbmath.org/1456.600182021-04-16T16:22:00+00:00"Ferrari, Patrik L."https://www.zbmath.org/authors/?q=ai:ferrari.patrik-lino"Frings, René"https://www.zbmath.org/authors/?q=ai:frings.reneKloosterman paths of prime powers moduli. II.https://www.zbmath.org/1456.112332021-04-16T16:22:00+00:00"Ricotta, Guillaume"https://www.zbmath.org/authors/?q=ai:ricotta.guillaume"Royer, Emmanuel"https://www.zbmath.org/authors/?q=ai:royer.emmanuel"Shparlinski, Igor"https://www.zbmath.org/authors/?q=ai:shparlinski.igor-eSummary: \textit{G. Ricotta} and \textit{E. Royer} [Comment. Math. Helv. 93, No. 3, 493--532 (2018; Zbl 1448.11214)] have recently proved that the polygonal paths joining the partial sums of the normalized classical Kloosterman sums \(S\left(a,b;p^n\right)/p^{n/2}\) converge in law in the Banach space of complex-valued continuous function on \([0,1]\) to an explicit random Fourier series as \((a,b)\) varies over \(\left(\mathbb{Z}/p^n\mathbb{Z}\right)^\times\times\left(\mathbb{Z}/p^n\mathbb{Z}\right)^\times,p\) tends to infinity among the odd prime numbers and \(n\geq 2\) is a fixed integer. This is the analogue of the result obtained by \textit{E.~Kowalski} and \textit{W. F. Sawin} [Compos. Math. 152, No. 7, 1489--1516 (2016; Zbl 1419.11134)] in the prime moduli case.
The purpose of this work is to prove a convergence law in this Banach space as only \(a\) varies over \(\left(\mathbb{Z}/p^n\mathbb{Z}\right)^\times,p\) tends to infinity among the odd prime numbers and \(n\geq 31\) is a fixed integer.Mode-coupling theory for multiple decay channels.https://www.zbmath.org/1456.828902021-04-16T16:22:00+00:00"Lang, Simon"https://www.zbmath.org/authors/?q=ai:lang.simon"Schilling, Rolf"https://www.zbmath.org/authors/?q=ai:schilling.rolf"Franosch, Thomas"https://www.zbmath.org/authors/?q=ai:franosch.thomasCommutator estimates from a viewpoint of regularity structures.https://www.zbmath.org/1456.352502021-04-16T16:22:00+00:00"Hoshino, Masato"https://www.zbmath.org/authors/?q=ai:hoshino.masatoSummary: First we introduce \textit{I. Bailleul} and the author's result, [``Paracontrolled calculus and regularity structures'', Preprint, \url{arXiv:1812.07919}], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator estimate \textit{I. Bailleul} and \textit{F. Bernicot} [Forum Math. Sigma 7, Paper No. e44, 94 p. (2019; Zbl 07139195)], which is a generalized version of the Gubinelli-Imkeller-Perkowski's commutator estimate [\textit{M. Gubinelli} et al., Forum Math. Pi 3, Paper No. e6, 75 p. (2015; Zbl 1333.60149), Lemma 2.4].Local asymptotics for the area under the random walk excursion.https://www.zbmath.org/1456.601082021-04-16T16:22:00+00:00"Perfilev, Elena"https://www.zbmath.org/authors/?q=ai:perfilev.elena"Wachtel, Vitali"https://www.zbmath.org/authors/?q=ai:wachtel.vitali-iSummary: We study the tail behaviour of the distribution of the area under the positive excursion of a random walk which has negative drift and light-tailed increments. We determine the asymptotics for local probabilities for the area and prove a local central limit theorem for the duration of the excursion conditioned on the large values of its area.Approximation of exit times for one-dimensional linear diffusion processes.https://www.zbmath.org/1456.602022021-04-16T16:22:00+00:00"Herrmann, Samuel"https://www.zbmath.org/authors/?q=ai:herrmann.samuel"Massin, Nicolas"https://www.zbmath.org/authors/?q=ai:massin.nicolasSummary: In order to approximate the exit time of a one-dimensional diffusion process, we propose an algorithm based on a random walk. Such an algorithm was already introduced in both the Brownian context and the Ornstein-Uhlenbeck context, that is for particular time-homogeneous diffusion processes. Here the aim is therefore to generalize this efficient numerical approach in order to obtain an approximation of both the exit time and position for a general linear diffusion. The main challenge of such a generalization is to handle with time-inhomogeneous diffusions. The efficiency of the method is described with particular care through theoretical results and numerical examples.Numerical solution of Itô-Volterra integral equation by least squares method.https://www.zbmath.org/1456.650052021-04-16T16:22:00+00:00"Ahmadinia, M."https://www.zbmath.org/authors/?q=ai:ahmadinia.mahdi|ahmadinia.mehdi"Afshari, A. H."https://www.zbmath.org/authors/?q=ai:afshari.a-h"Heydari, M."https://www.zbmath.org/authors/?q=ai:heydari.mahdi|heydari.mehdi|heydari.majeed|heydari.mohammad-taghi|heydari.mohammad-hossien|heydari.mohammadhossein|heydari.masoud|heydari.maryam|heydari.mohammad-mehdi|heydari.maysam|heydari.mojganSummary: This paper presents a computational method based on least squares method and block pulse functions for solving Itô-Volterra integral equation. The Itô-Volterra integral equation is converted to a linear system of algebraic equations by the least squares method on the block pulse functions. The error analysis of the proposed method is investigated by providing theorems. Numerical examples show the accuracy and reliability of the presented method. The numerical results confirm that the presented method is more accurate than the block pulse functions operational matrix method.Modified saddle-point integral near a singularity for the large deviation function.https://www.zbmath.org/1456.825942021-04-16T16:22:00+00:00"Lee, Jae Sung"https://www.zbmath.org/authors/?q=ai:lee.jaesung"Kwon, Chulan"https://www.zbmath.org/authors/?q=ai:kwon.chulan"Park, Hyunggyu"https://www.zbmath.org/authors/?q=ai:park.hyunggyuThe residual time approach for \((Q, r)\) model under perishability, general lead times, and lost sales.https://www.zbmath.org/1456.900082021-04-16T16:22:00+00:00"Barron, Yonit"https://www.zbmath.org/authors/?q=ai:barron.yonit"Baron, Opher"https://www.zbmath.org/authors/?q=ai:baron.opherSummary: We consider a \((Q, r)\) perishable inventory system with state-dependent compound Poisson demands with a random batch size, general lead times, exponential shelf times, and lost sales. We assume \(r < Q\) and analyze the system using an embedded Markov process at the replenishment points. Using the queueing and Markov chain decomposition approach, we characterize the distribution of the residual lead time and derive the stationary distribution of the inventory level. We construct closed-form expressions for the expected total long-run average cost function. The closed form allows us to efficiently obtain, numerically, the optimal \(Q\) and \(r\) parameters. Numerical study provides several guidelines for the optimal control. For example, we show that approximating the lead time distribution by an exponential one only works when the optimal reorder point of the approximation is very small; in other cases the usage of the exact distribution can lead to substantial cost savings (up to 14\%). We further provide intuition insight on the optimal controls and how they depend on different factors, e.g., the lead time variability, and the demand features (arrival rate, size and variability).A trace formula for activated escape in noisy maps.https://www.zbmath.org/1456.601702021-04-16T16:22:00+00:00"Demaeyer, J."https://www.zbmath.org/authors/?q=ai:demaeyer.jonathan"Gaspard, P."https://www.zbmath.org/authors/?q=ai:gaspard.pierreA conservative index heuristic for routing problems with multiple heterogeneous service facilities.https://www.zbmath.org/1456.900572021-04-16T16:22:00+00:00"Shone, Rob"https://www.zbmath.org/authors/?q=ai:shone.rob"Knight, Vincent A."https://www.zbmath.org/authors/?q=ai:knight.vincent-a"Harper, Paul R."https://www.zbmath.org/authors/?q=ai:harper.paul-rSummary: We consider a queueing system with \(N\) heterogeneous service facilities, in which admission and routing decisions are made when customers arrive and the objective is to maximize long-run average net rewards. For this type of problem, it is well-known that structural properties of optimal policies are difficult to prove in general and dynamic programming methods are computationally infeasible unless \(N\) is small. In the absence of an optimal policy to refer to, the Whittle index heuristic (originating from the literature on multi-armed bandit problems) is one approach which might be used for decision-making. After establishing the required indexability property, we show that the Whittle heuristic possesses certain structural properties which do not extend to optimal policies, except in some special cases. We also present results from numerical experiments which demonstrate that, in addition to being consistently strong over all parameter sets, the Whittle heuristic tends to be more robust than other heuristics with respect to the number of service facilities and the amount of heterogeneity between the facilities.Simulated likelihood estimators for discretely observed jump-diffusions.https://www.zbmath.org/1456.621702021-04-16T16:22:00+00:00"Giesecke, K."https://www.zbmath.org/authors/?q=ai:giesecke.kay"Schwenkler, Gustavo"https://www.zbmath.org/authors/?q=ai:schwenkler.gustavoSummary: This paper develops an unbiased Monte Carlo approximation to the transition density of a jump-diffusion process with state-dependent drift, volatility, jump intensity, and jump magnitude. The approximation is used to construct a likelihood estimator of the parameters of a jump-diffusion observed at fixed time intervals that need not be short. The estimator is asymptotically unbiased for any sample size. It has the same large-sample asymptotic properties as the true but uncomputable likelihood estimator. Numerical results illustrate its properties.On moving-average models with feedback.https://www.zbmath.org/1456.622042021-04-16T16:22:00+00:00"Li, Dong"https://www.zbmath.org/authors/?q=ai:li.dong.2"Ling, Shiqing"https://www.zbmath.org/authors/?q=ai:ling.shiqing"Tong, Howell"https://www.zbmath.org/authors/?q=ai:tong.howellSummary: Moving average models, linear or nonlinear, are characterized by their short memory. This paper shows that, in the presence of feedback in the dynamics, the above characteristic can disappear.On Bagchi-Pal urn models and related Pólya-Friedman ones.https://www.zbmath.org/1456.600322021-04-16T16:22:00+00:00"Huillet, Thierry E."https://www.zbmath.org/authors/?q=ai:huillet.thierry-eMay-Wigner transition in large random dynamical systems.https://www.zbmath.org/1456.601492021-04-16T16:22:00+00:00"Ipsen, J. R."https://www.zbmath.org/authors/?q=ai:ipsen.jesper-rThe tempered stable process with infinitely divisible inverse subordinators.https://www.zbmath.org/1456.828272021-04-16T16:22:00+00:00"Wyłomańska, Agnieszka"https://www.zbmath.org/authors/?q=ai:wylomanska.agnieszkaTruncated Euler-Maruyama method for classical and time-changed non-autonomous stochastic differential equations.https://www.zbmath.org/1456.650072021-04-16T16:22:00+00:00"Liu, Wei"https://www.zbmath.org/authors/?q=ai:liu.wei"Mao, Xuerong"https://www.zbmath.org/authors/?q=ai:mao.xuerong"Tang, Jingwen"https://www.zbmath.org/authors/?q=ai:tang.jingwen"Wu, Yue"https://www.zbmath.org/authors/?q=ai:wu.yueSummary: The truncated Euler-Maruyama (EM) method is proposed to approximate a class of non-autonomous stochastic differential equations (SDEs) with the Hölder continuity in the temporal variable and the super-linear growth in the state variable. The strong convergence with the convergence rate is proved. Moreover, the strong convergence of the truncated EM method for a class of highly non-linear time-changed SDEs is studied.Asymmetric Lévy flights in the presence of absorbing boundaries.https://www.zbmath.org/1456.601022021-04-16T16:22:00+00:00"de Mulatier, Clélia"https://www.zbmath.org/authors/?q=ai:de-mulatier.clelia"Rosso, Alberto"https://www.zbmath.org/authors/?q=ai:rosso.alberto"Schehr, Grégory"https://www.zbmath.org/authors/?q=ai:schehr.gregoryStochastic delocalization of finite populations.https://www.zbmath.org/1456.921162021-04-16T16:22:00+00:00"Geyrhofer, Lukas"https://www.zbmath.org/authors/?q=ai:geyrhofer.lukas"Hallatschek, Oskar"https://www.zbmath.org/authors/?q=ai:hallatschek.oskarSome results on the Brownian meander with drift.https://www.zbmath.org/1456.600902021-04-16T16:22:00+00:00"Iafrate, F."https://www.zbmath.org/authors/?q=ai:iafrate.francesco"Orsingher, E."https://www.zbmath.org/authors/?q=ai:orsingher.enzoSummary: In this paper we study the drifted Brownian meander that is a Brownian motion starting from \(u\) and subject to the condition that \(\min_{ 0\le z\le t}B(z)> v\) with \(u > v \). The limiting process for \(u\downarrow v\) is analysed, and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.On the probability that a stationary Gaussian process with spectral gap remains non-negative on a long interval.https://www.zbmath.org/1456.600782021-04-16T16:22:00+00:00"Feldheim, Naomi"https://www.zbmath.org/authors/?q=ai:feldheim.naomi-dvora"Feldheim, Ohad"https://www.zbmath.org/authors/?q=ai:feldheim.ohad-noy"Jaye, Benjamin"https://www.zbmath.org/authors/?q=ai:jaye.benjamin-j"Nazarov, Fedor"https://www.zbmath.org/authors/?q=ai:nazarov.fedor-l"Nitzan, Shahaf"https://www.zbmath.org/authors/?q=ai:nitzan.shahafSummary: Let \(f\) be a zero mean continuous stationary Gaussian process on \(\mathbb{R}\) whose spectral measure vanishes in a \(\delta \)-neighborhood of the origin. Then, the probability that \(f\) stays non-negative on an interval of length \(L\) is at most \(e^{-c\delta^2 L^2}\) with some absolute \(c>0\) and the result is sharp without additional assumptions.Bridges with random length: gamma case.https://www.zbmath.org/1456.600952021-04-16T16:22:00+00:00"Erraoui, Mohamed"https://www.zbmath.org/authors/?q=ai:erraoui.mohamed"Hilbert, Astrid"https://www.zbmath.org/authors/?q=ai:hilbert.astrid"Louriki, Mohammed"https://www.zbmath.org/authors/?q=ai:louriki.mohammedSummary: In this paper, we generalize the concept of gamma bridge in the sense that the length will be random, that is, the time to reach the given level is random. The main objective of this paper is to show that certain basic properties of gamma bridges with deterministic length stay true also for gamma bridges with random length. We show that the gamma bridge with random length is a pure jump process and that its jumping times are countable and dense in the random interval bounded by 0 and the random length. Moreover, we prove that this process is a Markov process with respect to its completed natural filtration as well as with respect to the usual augmentation of this filtration, which leads us to conclude that its completed natural filtration is right continuous. Finally, we give its canonical decomposition with respect to the usual augmentation of its natural filtration.Pinned diffusions and Markov bridges.https://www.zbmath.org/1456.600852021-04-16T16:22:00+00:00"Hildebrandt, Florian"https://www.zbmath.org/authors/?q=ai:hildebrandt.florian"Rœlly, Sylvie"https://www.zbmath.org/authors/?q=ai:roelly.sylvieSummary: In this article, we consider a family of real-valued diffusion processes on the time interval [0,1] indexed by their prescribed initial value \(x\in\mathbb{R}\) and another point in space, \(y\in\mathbb{R}\). We first present an \textit{easy-to-check} condition on their drift and diffusion coefficients ensuring that the diffusion is pinned in \(y\) at time \(t=1\). Our main result then concerns the following question: can this family of pinned diffusions be obtained as the bridges either of a Gaussian Markov process or of an Itô diffusion? We eventually illustrate our precise answer with several examples.Averages of products and ratios of characteristic polynomials in polynomial ensembles.https://www.zbmath.org/1456.600112021-04-16T16:22:00+00:00"Akemann, Gernot"https://www.zbmath.org/authors/?q=ai:akemann.gernot"Strahov, Eugene"https://www.zbmath.org/authors/?q=ai:strahov.eugene"Würfel, Tim R."https://www.zbmath.org/authors/?q=ai:wurfel.tim-rSummary: Polynomial ensembles are a sub-class of probability measures within determinantal point processes. Examples include products of independent random matrices, with applications to Lyapunov exponents, and random matrices with an external field, that may serve as schematic models of quantum field theories with temperature. We first analyse expectation values of ratios of an equal number of characteristic polynomials in general polynomial ensembles. Using Schur polynomials, we show that polynomial ensembles constitute Giambelli compatible point processes, leading to a determinant formula for such ratios as in classical ensembles of random matrices. In the second part, we introduce invertible polynomial ensembles given, e.g. by random matrices with an external field. Expectation values of arbitrary ratios of characteristic polynomials are expressed in terms of multiple contour integrals. This generalises previous findings by Fyodorov, Grela, and Strahov [\textit{Y. V. Fyodorov} et al., J. Phys. A, Math. Theor. 51, No. 13, Article ID 134003, 30 p. (2018; Zbl 1388.60025)]. for a single ratio in the context of eigenvector statistics in the complex Ginibre ensemble.Cramér moderate deviation expansion for martingales with one-sided Sakhanenko's condition and its applications.https://www.zbmath.org/1456.600982021-04-16T16:22:00+00:00"Fan, Xiequan"https://www.zbmath.org/authors/?q=ai:fan.xiequan"Grama, Ion"https://www.zbmath.org/authors/?q=ai:grama.ion-g"Liu, Quansheng"https://www.zbmath.org/authors/?q=ai:liu.quanshengSummary: We give a Cramér moderate deviation expansion for martingales with differences having finite conditional moments of order \(2+\rho,\rho\in(0,1]\), and finite one-sided conditional exponential moments. The upper bound of the range of validity and the remainder of our expansion are both optimal. Consequently, our result leads to a one-sided moderate deviation principle for martingales. Moreover, applications to quantile coupling inequality, \(\beta\)-mixing sequences and \(\psi\)-mixing sequences are discussed.Law of the first passage triple of a spectrally positive strictly stable process.https://www.zbmath.org/1456.601122021-04-16T16:22:00+00:00"Chi, Zhiyi"https://www.zbmath.org/authors/?q=ai:chi.zhiyiSummary: For a spectrally positive and strictly stable process with index in (1, 2), a series representation is obtained for the joint distribution of the ``first passage triple'' that consists of the time of first passage and the undershoot and the overshoot at first passage. The result leads to several corollaries, including (1) the joint law of the first passage triple and the pre-passage running supremum, and (2) at a fixed time point, the joint law of the process' value, running supremum, and the time of the running supremum. The representation can be decomposed as a sum of strictly positive functions that allow exact sampling of the first passage triple.Density bounds for solutions to differential equations driven by Gaussian rough paths.https://www.zbmath.org/1456.600842021-04-16T16:22:00+00:00"Gess, Benjamin"https://www.zbmath.org/authors/?q=ai:gess.benjamin"Ouyang, Cheng"https://www.zbmath.org/authors/?q=ai:ouyang.cheng"Tindel, Samy"https://www.zbmath.org/authors/?q=ai:tindel.samySummary: We consider finite-dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution for any fixed time \(t>0\). In addition, we provide Varadhan estimates for the asymptotic behavior of the density for small noise. The emphasis is on working with general Gaussian processes with covariance function satisfying suitable abstract, checkable conditions.Peculiar spectral statistics of ensembles of trees and star-like graphs.https://www.zbmath.org/1456.051072021-04-16T16:22:00+00:00"Kovaleva, V."https://www.zbmath.org/authors/?q=ai:kovaleva.v-s|kovaleva.v-v|kovaleva.viktoria-a"Maximov, Yu."https://www.zbmath.org/authors/?q=ai:maksimov.yu-i|maximov.yury|maksimov.yu-m|maksimov.yu-v"Nechaev, S."https://www.zbmath.org/authors/?q=ai:nechaev.sergei-k"Valba, O."https://www.zbmath.org/authors/?q=ai:valba.olga-vAdvances in stabilization of hybrid stochastic differential equations by delay feedback control.https://www.zbmath.org/1456.601482021-04-16T16:22:00+00:00"Hu, Junhao"https://www.zbmath.org/authors/?q=ai:hu.junhao"Liu, Wei"https://www.zbmath.org/authors/?q=ai:liu.wei"Deng, Feiqi"https://www.zbmath.org/authors/?q=ai:deng.feiqi"Mao, Xuerong"https://www.zbmath.org/authors/?q=ai:mao.xuerongSharp bounds for the variance of linear statistics on random permutations.https://www.zbmath.org/1456.600342021-04-16T16:22:00+00:00"Manstavičius, Eugenijus"https://www.zbmath.org/authors/?q=ai:manstavicius.eugenijusSummary: We are concerned with the variance of a completely additive function defined on the symmetric group endowed with the Ewens probability. Overcoming specific dependence of the summands, we obtain the upper and lower bounds including optimal constants. We also derive a decomposition of such a function into a sum with uncorrelated summands. The results can be reformulated for the linear statistics defined on vectors distributed according to the Ewens sampling formula.Effective bandwidth of non-Markovian packet traffic.https://www.zbmath.org/1456.940032021-04-16T16:22:00+00:00"Cavallaro, Massimo"https://www.zbmath.org/authors/?q=ai:cavallaro.massimo"Harris, Rosemary J."https://www.zbmath.org/authors/?q=ai:harris.rosemary-jReliability analysis of multi-state two-dimensional system by universal generating function.https://www.zbmath.org/1456.602362021-04-16T16:22:00+00:00"Meenakshi, K."https://www.zbmath.org/authors/?q=ai:meenakshi.k-n"Singh, S. B."https://www.zbmath.org/authors/?q=ai:singh.suresh-b|singh.saket-bihari|singh.suraj-bhanSummary: In this paper, two dimensional multi-state non-repairable systems having \(m\) rows and \(n\) columns have been studied. Markov stochastic process has been applied for obtaining probabilities of the components. Reliability metrics such as reliability, mean time to failure and sensitivity analysis of the target system with the application of universal generating function are evaluated. Finally, the developed model is demonstrated with the help of a numerical example.
For the entire collection see [Zbl 1446.65004].Nonlocal birth-death competitive dynamics with volume exclusion.https://www.zbmath.org/1456.920442021-04-16T16:22:00+00:00"Khalil, Nagi"https://www.zbmath.org/authors/?q=ai:khalil.nagi"López, Cristóbal"https://www.zbmath.org/authors/?q=ai:lopez.cristobal"Hernández-García, Emilio"https://www.zbmath.org/authors/?q=ai:hernandez-garcia.emilioLévy noise-induced escape in an excitable system.https://www.zbmath.org/1456.920292021-04-16T16:22:00+00:00"Cai, Rui"https://www.zbmath.org/authors/?q=ai:cai.rui"Chen, Xiaoli"https://www.zbmath.org/authors/?q=ai:chen.xiaoli"Duan, Jinqiao"https://www.zbmath.org/authors/?q=ai:duan.jinqiao"Kurths, Jürgen"https://www.zbmath.org/authors/?q=ai:kurths.jurgen"Li, Xiaofan"https://www.zbmath.org/authors/?q=ai:li.xiaofanAgreement dynamics on directed random graphs.https://www.zbmath.org/1456.602602021-04-16T16:22:00+00:00"Lipowski, Adam"https://www.zbmath.org/authors/?q=ai:lipowski.adam"Lipowska, Dorota"https://www.zbmath.org/authors/?q=ai:lipowska.dorota"Ferreira, António Luis"https://www.zbmath.org/authors/?q=ai:ferreira.antonio-luisGeneralized \(k\)-core pruning process on directed networks.https://www.zbmath.org/1456.051632021-04-16T16:22:00+00:00"Zhao, Jin-Hua"https://www.zbmath.org/authors/?q=ai:zhao.jinhuaSpectra of large time-lagged correlation matrices from random matrix theory.https://www.zbmath.org/1456.600272021-04-16T16:22:00+00:00"Nowak, Maciej A."https://www.zbmath.org/authors/?q=ai:nowak.maciej-a"Tarnowski, Wojciech"https://www.zbmath.org/authors/?q=ai:tarnowski.wojciechStatistical characterization of the standard map.https://www.zbmath.org/1456.370102021-04-16T16:22:00+00:00"Ruiz, Guiomar"https://www.zbmath.org/authors/?q=ai:ruiz.guiomar"Tirnakli, Ugur"https://www.zbmath.org/authors/?q=ai:tirnakli.ugur"Borges, Ernesto P."https://www.zbmath.org/authors/?q=ai:borges.ernesto-p"Tsallis, Constantino"https://www.zbmath.org/authors/?q=ai:tsallis.constantinoAbelian oil and water dynamics does not have an absorbing-state phase transition.https://www.zbmath.org/1456.602512021-04-16T16:22:00+00:00"Candellero, Elisabetta"https://www.zbmath.org/authors/?q=ai:candellero.elisabetta"Stauffer, Alexandre"https://www.zbmath.org/authors/?q=ai:stauffer.alexandre-o"Taggi, Lorenzo"https://www.zbmath.org/authors/?q=ai:taggi.lorenzoSummary: The oil and water model is an interacting particle system with two types of particles and a dynamics that conserves the number of particles, which belongs to the so-called class of Abelian networks. Widely studied processes in this class are sandpiles models and activated random walks, which are known (at least for some choice of the underlying graph) to undergo an absorbing-state phase transition. This phase transition characterizes the existence of two regimes, depending on the particle density: a regime of fixation at low densities, where the dynamics converges towards an absorbing state and each particle jumps only finitely many times, and a regime of activity at large densities, where particles jump infinitely often and activity is sustained indefinitely. In this work we show that the oil and water model is substantially different than sandpiles models and activated random walks, in the sense that it does not undergo an absorbing-state phase transition and is in the regime of fixation at all densities. Our result works in great generality: for any graph that is vertex transitive and for a large class of initial configurations.Mean first passage times for piecewise deterministic Markov processes and the effects of critical points.https://www.zbmath.org/1456.601842021-04-16T16:22:00+00:00"Bressloff, Paul C."https://www.zbmath.org/authors/?q=ai:bressloff.paul-c"Lawley, Sean D."https://www.zbmath.org/authors/?q=ai:lawley.sean-dMotif statistics and spike correlations in neuronal networks.https://www.zbmath.org/1456.920302021-04-16T16:22:00+00:00"Hu, Yu"https://www.zbmath.org/authors/?q=ai:hu.yu"Trousdale, James"https://www.zbmath.org/authors/?q=ai:trousdale.james"Josić, Krešimir"https://www.zbmath.org/authors/?q=ai:josic.kresimir"Shea-Brown, Eric"https://www.zbmath.org/authors/?q=ai:shea-brown.ericMulti-coloured jigsaw percolation on random graphs.https://www.zbmath.org/1456.051412021-04-16T16:22:00+00:00"Cooley, Oliver"https://www.zbmath.org/authors/?q=ai:cooley.oliver"Gutierrez, Abraham"https://www.zbmath.org/authors/?q=ai:gutierrez.abrahamSummary: The jigsaw percolation process, introduced by \textit{C. D. Brummitt} et al. [Ann. Appl. Probab. 25, No. 4, 2013--2038 (2015; Zbl 1322.60210)], was inspired by a group of people collectively solving a puzzle. It can also be seen as a measure of whether two graphs on a common vertex set are ``jointly connected''. In this paper we consider the natural generalisation of this process to an arbitrary number of graphs on the same vertex set. We prove that if these graphs are random, then the jigsaw percolation process exhibits a phase transition in terms of the product of the edge probabilities. This generalises a result of \textit{B. Bollobás} et al. [Electron. J. Comb. 24, No. 2, Research Paper P2.36, 14 p. (2017; Zbl 1366.05096)].A proof of Sznitman's conjecture about ballistic RWRE.https://www.zbmath.org/1456.602712021-04-16T16:22:00+00:00"Guerra, Enrique"https://www.zbmath.org/authors/?q=ai:guerra.enrique"Ramírez, Alejandro F."https://www.zbmath.org/authors/?q=ai:ramirez.alejandro-fSummary: We consider random walk in a uniformly elliptic i.i.d. random environment in \(\mathbb{Z}^d\) for \(d \geq 2\). It is believed that whenever the random walk is transient in a given direction it is necessarily ballistic. In order to quantify the gap which would be needed to prove this equivalence, several ballisticity conditions have been introduced. In particular, Sznitman defined the so-called conditions \((T)\) and \((T')\). The first one is the requirement that certain unlikely exit probabilities from a set of slabs decay exponentially fast with their width \(L\). The second one is the requirement that for all \(\gamma \in (0, 1)\) condition \((T)_\gamma\) is satisfied, which in turn is defined as the requirement that the decay is like \(e^{-CL^\gamma}\) for some \(C > 0\). In this article we prove a conjecture of \textit{A.-S. Sznitman} from [Probab. Theory Relat. Fields 122, No. 4, 509--544 (2002; Zbl 0995.60097)], stating that \((T)\) and \((T')\) are equivalent. Hence, this closes the circle proving the equivalence of conditions \((T), (T')\), and \((T)_\gamma\) for some \(\gamma \in (0, 1)\) as conjectured by Sznitman, and also of each of these ballisticity conditions with the polynomial condition \((P)_M\) for \(M \geq 15d + 5\) introduced by \textit{N. Berger} et al. in [Commun. Pure Appl. Math. 67, No. 12, 1947--1973 (2014; Zbl 1364.60140)].A driven tagged particle in symmetric exclusion processes with removals.https://www.zbmath.org/1456.602672021-04-16T16:22:00+00:00"Wang, Zhe"https://www.zbmath.org/authors/?q=ai:wang.zheSummary: We consider a driven tagged particle in a symmetric exclusion process on \(\mathbb{Z}\) with a removal rule. In this process, untagged particles are removed once they jump to the left of the tagged particle. We investigate the behavior of the displacement of the tagged particle and prove limit theorems of it: an (annealed) law of large numbers, a central limit theorem, and a large deviation principle. We also characterize a class of ergodic measures for the environment process. Our approach is based on analyzing two auxiliary processes with associated martingales and a regenerative structure.Explicit construction of RIP matrices is Ramsey-hard.https://www.zbmath.org/1456.600202021-04-16T16:22:00+00:00"Gamarnik, David"https://www.zbmath.org/authors/?q=ai:gamarnik.davidSummary: Matrices \(\Phi \in \mathbb{R}^{n \times p}\) satisfying the restricted isometry property (RIP) are an important ingredient of the compressive sensing methods. While it is known that random matrices satisfy the RIP with high probability even for \(n = \log^{O(1)}p\), the explicit deteministic construction of such matrices defied the repeated efforts, and most of the known approaches hit the so-called \(\sqrt n\) sparsity bottleneck. The notable exception is the work by \textit{J. Bourgain} et al. [Duke Math. J. 159, No. 1, 145--185 (2011; Zbl 1236.94027)] constructing an \(n \times p\) RIP matrix with sparsity \(s = \Theta (n^{1/2 + \epsilon} )\), but in the regime \(n = \Omega (p^{1 - \delta} )\).
In this short note we resolve this open question by showing that an explicit construction of a matrix satisfying the RIP in the regime \(n = O(\log^2 p)\) and \(s = \Theta (n^{1/2})\) implies an explicit construction of a three-colored Ramsey graph on \(p\) nodes with clique sizes bounded by \(O(\log^2 p)\) -- a question in the field of extremal combinatorics that has been open for decades.Self-avoiding walk on the complete graph.https://www.zbmath.org/1456.824512021-04-16T16:22:00+00:00"Slade, Gordon"https://www.zbmath.org/authors/?q=ai:slade.gordonThe phase transition for self-avoiding walks on the complete graph is studied.
It is found that the susceptibility, i.e., the generating function that counts
the number of self-avoiding walks according to their length, can be expressed
explicitly in terms of the incomplete gamma function. As long as the graph is
finite, the susceptibility is just a polynomial. Therefore, the asymptotic
behavior of the susceptibility is of interest, which is obtained from the
asymptotic behavior of the incomplete gamma function. The latter has a
transition in its asymptotic behavior, which in turn yields a phase transition
for the susceptibility. As main result, a critical scaling window for this
phase transition is identified, and the different behaviors are described that
occur below, above, and within the critical window.
Reviewer: Christoph Koutschan (Linz)3D tamed Navier-Stokes equations driven by multiplicative Lévy noise: existence, uniqueness and large deviations.https://www.zbmath.org/1456.601592021-04-16T16:22:00+00:00"Dong, Zhao"https://www.zbmath.org/authors/?q=ai:dong.zhao"Zhang, Rangrang"https://www.zbmath.org/authors/?q=ai:zhang.rangrangSummary: In this paper, we show the existence and uniqueness of a strong solution to stochastic 3D tamed Navier-Stokes equations driven by multiplicative Lévy noise with periodic boundary conditions. Then we establish the large deviation principles of the strong solution on the state space \(\mathcal{D}([0, T]; \mathbb{H}^1)\), where the weak convergence approach plays a key role.The fundamental solution to 1D degenerate diffusion equation with one-sided boundary.https://www.zbmath.org/1456.602002021-04-16T16:22:00+00:00"Chen, Linan"https://www.zbmath.org/authors/?q=ai:chen.linan"Weih-Wadman, Ian"https://www.zbmath.org/authors/?q=ai:weih-wadman.ianSummary: In this work we adopt a combination of probabilistic approach and analytic method to study the fundamental solution to a certain type of one-dimensional degenerate diffusion equation. To be specific, we consider a diffusion equation on \((0, \infty)\) whose diffusion coefficient vanishes at the boundary 0, equipped with the Cauchy initial data and the Dirichlet boundary condition. One such diffusion equation that has been extensively studied is the one whose diffusion coefficient vanishes linearly at 0. Our main goal is to extend the study to cases when the diffusion coefficient has a general order of degeneracy, with a primary focus on the fundamental solution to such a degenerate diffusion equation. In particular, we study the regularity properties of the fundamental solution near 0, and investigate how the order of degeneracy of the diffusion operator and the Dirichlet boundary condition jointly affect these properties. We also provide estimates for the fundamental solution and its derivatives near 0.Analytic-geometric methods for finite Markov chains with applications to quasi-stationarity.https://www.zbmath.org/1456.601762021-04-16T16:22:00+00:00"Diaconis, Persi"https://www.zbmath.org/authors/?q=ai:diaconis.persi-w"Houston-Edwards, Kelsey"https://www.zbmath.org/authors/?q=ai:houston-edwards.kelsey"Saloff-Coste, Laurent"https://www.zbmath.org/authors/?q=ai:saloff-coste.laurentSummary: For a relatively large class of well-behaved absorbing (or killed) finite Markov chains, we give detailed quantitative estimates regarding the behavior of the chain before it is absorbed (or killed). Typical examples are random walks on boxlike finite subsets of the square lattice \(\mathbb{Z}^d\) absorbed (or killed) at the boundary. The analysis is based on Poincaré, Nash, and Harnack inequalities, moderate growth, and on the notions of John and inner-uniform domains.Sum rules for effective resistances in infinite graphs.https://www.zbmath.org/1456.051492021-04-16T16:22:00+00:00"Markowsky, Greg"https://www.zbmath.org/authors/?q=ai:markowsky.greg-t"Palacios, José Luis"https://www.zbmath.org/authors/?q=ai:palacios.jose-luisWork and heat distributions for a Brownian particle subjected to an oscillatory drive.https://www.zbmath.org/1456.827902021-04-16T16:22:00+00:00"Saha, Bappa"https://www.zbmath.org/authors/?q=ai:saha.bappa"Mukherji, Sutapa"https://www.zbmath.org/authors/?q=ai:mukherji.sutapaLarge fluctuations and fixation in evolutionary games.https://www.zbmath.org/1456.910112021-04-16T16:22:00+00:00"Assaf, Michael"https://www.zbmath.org/authors/?q=ai:assaf.michael"Mobilia, Mauro"https://www.zbmath.org/authors/?q=ai:mobilia.mauroFirst-passage time distribution for a random Walker on a random forcing energy landscape.https://www.zbmath.org/1456.824192021-04-16T16:22:00+00:00"Sheinman, Michael"https://www.zbmath.org/authors/?q=ai:sheinman.michael"Bénichou, Olivier"https://www.zbmath.org/authors/?q=ai:benichou.olivier"Voituriez, Raphaël"https://www.zbmath.org/authors/?q=ai:voituriez.raphael"Kafri, Yariv"https://www.zbmath.org/authors/?q=ai:kafri.yarivOn a retrial production inventory system with vacation and multiple servers.https://www.zbmath.org/1456.602422021-04-16T16:22:00+00:00"Jose, K. P."https://www.zbmath.org/authors/?q=ai:jose.k-p"Beena, P."https://www.zbmath.org/authors/?q=ai:beena.pSummary: In this paper, the model of a production inventory system with heterogeneous servers, the vacation of one of the servers (vacationing server), and retrial customers is considered. The customers reach the system each demanding exactly one unit of the item, according to a Poisson process. Service times and lead time are independent and follow exponential distributions. A single unit of the item is produced at a time according to (s, S) policy. It is assumed that when the inventory level reaches zero or when the orbit is empty or both, one of the servers (server 2) takes multiple, exponentially distributed vacation time. At the end of the vacation, that server immediately takes another vacation, if he/she finds empty stock or empty orbit or both. During the stock out period or server busy period or vacation period, the demands that arrive enter into the orbit of infinite size. If a customer finds both the servers busy or server 1 busy and server 2 in vacation or inventory level is zero, in accordance with Bernoulli trials may wait in the orbit or leave forever. When either the customer in the orbit cannot make an attempt due to the busy servers or inventory level zero, he/she under Bernoulli trials may come back to the orbit or leave the orbit. The rate of retrial customers from orbit is linear. The production process is switched on when the inventory level reaches to s, and similarly when the level of inventory reaches back to S the production process is switched off. The production process releases items that have inter arrival times that are exponentially distributed. Ergodicity condition is obtained and matrix analytic method is used to calculate the steady-state probabilities of the constructed 4D Markov chain. Minimum expected total cost per unit time and many significant system performance measures are obtained. Sensitivity analysis is relevant to check various performance measures that is highly applicable in the realistic situation and it also provides managerial insights.Splitting methods for Fokker-Planck equations related to jump-diffusion processes.https://www.zbmath.org/1456.650662021-04-16T16:22:00+00:00"Gaviraghi, Beatrice"https://www.zbmath.org/authors/?q=ai:gaviraghi.beatrice"Annunziato, Mario"https://www.zbmath.org/authors/?q=ai:annunziato.mario"Borzì, Alfio"https://www.zbmath.org/authors/?q=ai:borzi.alfioSummary: A splitting implicit-explicit (SIMEX) scheme for solving a partial integro-differential Fokker-Planck equation related to a jump-diffusion process is investigated. This scheme combines the method of Chang-Cooper for spatial discretization with the Strang-Marchuk splitting and first- and second-order time discretization methods. It is proven that the SIMEX scheme is second-order accurate, positive preserving, and conservative. Results of numerical experiments that validate the theoretical results are presented. (This chapter is a summary of the paper [\textit{B. Gaviraghi} et al., Appl. Math. Comput. 294, 1--17 (2017; Zbl 1411.65110)]; all theoretical statements in this summary are proved in that reference.)
For the entire collection see [Zbl 1390.91011].A Geo/Geo/1 inventory priority queue with self induced interruption.https://www.zbmath.org/1456.900072021-04-16T16:22:00+00:00"Anilkumar, M. P."https://www.zbmath.org/authors/?q=ai:anilkumar.m-p"Jose, K. P."https://www.zbmath.org/authors/?q=ai:jose.k-pSummary: This paper considers discrete time \((s, S)\) inventory Geo/Geo/1 priority queue formed by the customers' induced interruption during service. An arriving customer enters into a high priority queue of infinite capacity. During his/her service, the service may be interrupted due to own reasons with some probability. The interrupted customer is moved to a lower priority queue of infinite capacity. An item in the inventory is supplied whenever a customer leaves from high priority queue after interrupting/completing the service. The customer in the lower priority queue is served according to preemptive priority discipline. Inter-arrival time, service time and lead time are considered to be geometrically distributed. We use the matrix analytic method to analyse the model. The necessary and sufficient condition for the stability of the system is obtained. The marginal distributions of both higher and lower priority queue lengths are studied. Numerical experiments are incorporated to draw special attention to the importance of the model.Numerical solution of backward fuzzy SDEs with time delayed coefficients.https://www.zbmath.org/1456.650092021-04-16T16:22:00+00:00"Zabiba, Mohammed S."https://www.zbmath.org/authors/?q=ai:zabiba.mohammed-s"Falah, Sarhan"https://www.zbmath.org/authors/?q=ai:falah.sarhanSummary: In this work, we consider the fuzzy stochastic differential delay equation and study the numerical solution of backward fuzzy stochastic differential delay equations (FSDDEs). Finally, we examine numerical convergence for FSDDEs.Two-way communication orbit queues with server vacation.https://www.zbmath.org/1456.602392021-04-16T16:22:00+00:00"Dey, Sweta"https://www.zbmath.org/authors/?q=ai:dey.sweta"Deepak, T. G."https://www.zbmath.org/authors/?q=ai:deepak.t-gSummary: We consider a single server retrial model with two streams of calls namely, incoming and outgoing calls. Each stream consists of multiple classes of calls. As part of the internal work load, presence of outgoing calls are always assumed in the system. Arrival of incoming calls obey the Poisson law. Upon seeing a busy server at its arrival epoch, an incoming call will be directed to an orbit according to the class it belongs to and tries to get an idle sever in gap of exponential amount of time with class dependent mean. Similar kind of attempt is being made by the outgoing calls also to reach an idle server. Once the sever becomes idle, if neither an incoming nor an outgoing call turns up for an exponential amount of time, the server goes for vacation and the vacation time is assumed to be exponential. Within each stream, service times of multiple classes of calls are assumed to be independent exponential with class dependent means. Matrix Analytic Method and regenerative approach are used to derive the explicit form of the steady state probabilities. Many performance measures are computed to analyse the system performance.Large-sample variance of simulation using refined descriptive sampling: case of independent variables.https://www.zbmath.org/1456.600042021-04-16T16:22:00+00:00"Baiche, Leila"https://www.zbmath.org/authors/?q=ai:baiche.leila"Ourbih-Tari, Megdouda"https://www.zbmath.org/authors/?q=ai:ourbih-tari.megdoudaSummary: Derived from descriptive sampling (DS) as a better approach to Monte Carlo simulation, refined DS is a method of sampling that can be used to produce input values for estimation of expectations of functions of output variables. In this article, the asymptotic variance of such an estimate in case of independent input variables is obtained and it was shown that asymptotically, the variance is less than that obtained using simple random sampling.Numerical study of Schramm-Loewner evolution in the random 3-state Potts model.https://www.zbmath.org/1456.821012021-04-16T16:22:00+00:00"Chatelain, C."https://www.zbmath.org/authors/?q=ai:chatelain.clement|chatelain.christopheTransient analysis of a Markov queueing model with feedback, discouragement and disaster.https://www.zbmath.org/1456.602412021-04-16T16:22:00+00:00"Jain, Madhu"https://www.zbmath.org/authors/?q=ai:jain.madhu"Singh, Mayank"https://www.zbmath.org/authors/?q=ai:singh.mayankSummary: The transient model for a Markovian feedback queue with system disaster and customer impatient has been investigated. After service completion, dissatisfied customers can feedback to the system to get another service. During the service, the system may suffer disaster failure and consequently lose all the customers present in the system. After the occurrence of a disaster, the system immediately goes under the repair process. During the repair, the newly arriving customers may get discouraged and balk without joining the queue. Upon arrival in the down state of the system, the arriving customers activate their individual timer. A customer waiting in the queue departs and never comes back if the timer run out before the system gets repaired. The time-dependent system size distribution is formulated analytically by applying the techniques of probability generating function along with continued fractions. The computational results are presented in graphical and tabular form to examine the variation of system descriptors on various performance indices.A path integral approach to age dependent branching processes.https://www.zbmath.org/1456.921172021-04-16T16:22:00+00:00"Greenman, Chris D."https://www.zbmath.org/authors/?q=ai:greenman.chris-dVolatility estimation and jump detection for drift-diffusion processes.https://www.zbmath.org/1456.622512021-04-16T16:22:00+00:00"Laurent, Sébastien"https://www.zbmath.org/authors/?q=ai:laurent.sebastien-yves"Shi, Shuping"https://www.zbmath.org/authors/?q=ai:shi.shupingSummary: The logarithmic prices of financial assets are conventionally assumed to follow a drift-diffusion process. While the drift term is typically ignored in the infill asymptotic theory and applications, the presence of temporary nonzero drifts is an undeniable fact. The finite sample theory for integrated variance estimators and extensive simulations provided in this paper reveal that the drift component has a nonnegligible impact on the estimation accuracy of volatility, which leads to a dramatic power loss for a class of jump identification procedures. We propose an alternative construction of volatility estimators and observe significant improvement in the estimation accuracy in the presence of nonnegligible drift. The analytical formulas of the finite sample bias of the realized variance, bipower variation, and their modified versions take simple and intuitive forms. The new jump tests, which are constructed from the modified volatility estimators, show satisfactory performance. As an illustration, we apply the new volatility estimators and jump tests, along with their original versions, to 21 years of 5-minute log returns of the NASDAQ stock price index.Exact solution of a two-type branching process: clone size distribution in cell division kinetics.https://www.zbmath.org/1456.602292021-04-16T16:22:00+00:00"Antal, Tibor"https://www.zbmath.org/authors/?q=ai:antal.tibor"Krapivsky, P. L."https://www.zbmath.org/authors/?q=ai:krapivsky.pavel-lVariational and optimal control representations of conditioned and driven processes.https://www.zbmath.org/1456.930072021-04-16T16:22:00+00:00"Chetrite, Raphaël"https://www.zbmath.org/authors/?q=ai:chetrite.raphael"Touchette, Hugo"https://www.zbmath.org/authors/?q=ai:touchette.hugoFirst-passage properties of the Pólya urn process.https://www.zbmath.org/1456.600292021-04-16T16:22:00+00:00"Antal, Tibor"https://www.zbmath.org/authors/?q=ai:antal.tibor"Ben-Naim, E."https://www.zbmath.org/authors/?q=ai:ben-naim.eli"Krapivsky, P. L."https://www.zbmath.org/authors/?q=ai:krapivsky.pavel-lTime-dependent probability density functions and information geometry in stochastic logistic and Gompertz models.https://www.zbmath.org/1456.620242021-04-16T16:22:00+00:00"Tenkès, Lucille-Marie"https://www.zbmath.org/authors/?q=ai:tenkes.lucille-marie"Hollerbach, Rainer"https://www.zbmath.org/authors/?q=ai:hollerbach.rainer"Kim, Eun-Jin"https://www.zbmath.org/authors/?q=ai:kim.eunjinAttractiveness and exponential \(p\)-stability of neutral stochastic functional integro-differential equations driven by Wiener process and fBm with impulses effects.https://www.zbmath.org/1456.601732021-04-16T16:22:00+00:00"Hamit, Mahamat Hassan Mahamat"https://www.zbmath.org/authors/?q=ai:hamit.mahamat-hassan-mahamat"Allognissode, Fulbert Kuessi"https://www.zbmath.org/authors/?q=ai:allognissode.fulbert-kuessi"Mohamed, Mohamed salem"https://www.zbmath.org/authors/?q=ai:mohamed.mohamed-salem"Issaka, Louk-Man"https://www.zbmath.org/authors/?q=ai:issaka.louk-man"Diop, Mamadou Abdoul"https://www.zbmath.org/authors/?q=ai:diop.mamadou-abdoulSummary: In this work, we consider a class of neutral stochastic integro-differential equations driven by Wiener process and fractional Brownian motion with impulses effects. This paper deals with the global attractiveness and quasi-invariant sets for neutral stochastic integro-differential equations driven by Wiener process and fractional Brownian motion with impulses effects in Hilbert spaces. We use new integral inequalities combined with theories of resolvent operators to establish a set of sufficient conditions for the exponential \(p\)-stability of the mild solution of the considered equations. An example is presented to demonstrate the obtained theory.Data assimilation and parameter estimation for a multiscale stochastic system with \(\alpha \)-stable Lévy noise.https://www.zbmath.org/1456.600932021-04-16T16:22:00+00:00"Zhang, Yanjie"https://www.zbmath.org/authors/?q=ai:zhang.yanjie"Cheng, Zhuan"https://www.zbmath.org/authors/?q=ai:cheng.zhuan"Zhang, Xinyong"https://www.zbmath.org/authors/?q=ai:zhang.xinyong"Chen, Xiaoli"https://www.zbmath.org/authors/?q=ai:chen.xiaoli"Duan, Jinqiao"https://www.zbmath.org/authors/?q=ai:duan.jinqiao"Li, Xiaofan"https://www.zbmath.org/authors/?q=ai:li.xiaofanNoise-enhanced stability and double stochastic resonance of active Brownian motion.https://www.zbmath.org/1456.602222021-04-16T16:22:00+00:00"Zeng, Chunhua"https://www.zbmath.org/authors/?q=ai:zeng.chunhua"Zhang, Chun"https://www.zbmath.org/authors/?q=ai:zhang.chun"Zeng, Jiakui"https://www.zbmath.org/authors/?q=ai:zeng.jiakui"Liu, Ruifen"https://www.zbmath.org/authors/?q=ai:liu.ruifen"Wang, Hua"https://www.zbmath.org/authors/?q=ai:wang.hua.1|wang.hua|wang.hua.2The fluctuation theorem for currents in semi-Markov processes.https://www.zbmath.org/1456.825412021-04-16T16:22:00+00:00"Andrieux, David"https://www.zbmath.org/authors/?q=ai:andrieux.david"Gaspard, Pierre"https://www.zbmath.org/authors/?q=ai:gaspard.pierre