Recent zbMATH articles in MSC 60Jhttps://www.zbmath.org/atom/cc/60J2021-04-16T16:22:00+00:00WerkzeugDiscovering 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}Large 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.mauroReduction 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.raulJoint 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.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.claudeDelay 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.stefanInfinitely 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)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.emilioRare 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.angeloAnalysis 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)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.ralfBeyond 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.pingMean 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-dGradual 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.olivierArithmetic 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.stephaneA 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.katjaKernel 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 \(a_n=\sqrt n\).Extinction 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.michelModelling 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.Integral 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.frankModeling 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-pMoments 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)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-aliJoint 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.danielContinuity 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.Directed, 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.Geometric 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.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-luisGeneralized 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.shilongSplitting 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].Diffusion 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.gyorgyModeling 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.grzegorzNoise-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.2Entropy 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.hayeA 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-dTightness 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.oferLarge-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.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.Stability 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.rudiDiscovering 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.5Distribution 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.gleb\(L^q(L^p)\)-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 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-geutherAverage 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.oksanaThe 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'' \(N \to \infty\).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-aliTwo-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.Limiting 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.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.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.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-cIntermediate-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.sidneyBoundary 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].Rapid 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)].Optimal 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.sidneyA 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.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.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.jiulinStatistics 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.Hyperbolic 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.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.peiThe 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.30Random 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.lucianoRandom 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-geronimoPiecewise 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].Asymptotics 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.guangyingTwo-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.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-albertoLimit 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-mAnalytic-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.Exact 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.chinkunMixing 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.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.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.jaeyoungStability 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.Hydrodynamic 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.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.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.Stochastic 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.oskarA 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)The 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.pierreDispersion 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.xianbinEvolutionary 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-iHigher 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)Occupation 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.jeanMutual 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.massimilianoQuantum 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-jHidden 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-gVariational 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.hugoTowards 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.derekLight 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.robertControl 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.rajeshOn 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.donPATRICIA 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.antonMarkovian 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.antonThe 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.andreasSLE 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.kalleCorrelation 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.vladimirNonlocal 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.vivienBook 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].Connectivity 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.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.luigiOn 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)Stationary 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.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.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)].Anomalous 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 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.Some 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.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.2Komatu-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)Fractal 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-renataBridges 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.Extracting 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}Response 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.stephanThe 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-jMutant 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.tiborMacroscopic 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.haoPinned 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.Stopping 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)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.stefaniaAn 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.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-tamasKingman'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.Exact 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.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.vygintasOn 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].Work 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.sutapaLinear 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.christianOscillation 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.Subcritical 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-eAlgebraic 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.stephaneUnbiased 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 \((\alpha,\beta)\).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.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.nunoScalings 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.eunjinThe 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.herbertOn 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)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.gatienNumerical 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.christopheExact 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-lEquilibrium 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].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-pHidden 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.Time-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.marcosOn 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.paoloOn 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-ivanovichGaussian 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.piotrRemarks 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.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.Non-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.fredericHydrodynamically 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.baoquanApplication 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.Anomalous 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.dongchengExistence 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.Volatility 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.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).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.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-eEstimates 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.Asymptotics 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.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.Minimax 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.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.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-bornOverdamped 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.agostinoThe 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)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.marcoAdvances 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.xuerong