Recent zbMATH articles in MSC 60G https://www.zbmath.org/atom/cc/60G 2022-06-24T15:10:38.853281Z Werkzeug Improved mixing rates of directed cycles by added connection https://www.zbmath.org/1485.05164 2022-06-24T15:10:38.853281Z "Gerencsér, Balázs" https://www.zbmath.org/authors/?q=ai:gerencser.balazs "Hendrickx, Julien M." https://www.zbmath.org/authors/?q=ai:hendrickx.julien-m The theme of this paper is the effect that the addition of random edges and non-reversibility have on the mixing time of a random walk on a graph. This is studied on a cycle of $$n$$ vertices. Thereon, $$k$$ disjoint paths are selected randomly and they are directed in the clockwise direction. For any two of them, the edges between the end of one and the beginning of the other are added. So if the particle that performs this random walk is at the beginning of such a path and chooses to follow the path the next hub (in the clockwise direction), it follows it all the way until its end in the clockwise direction with probability 1. If it choose to jump it selects the beginning of another interval selected uniformly at random. The parameter $$k$$ depends on $$n$$ and, in particular, it is set to $$n^{\sigma}$$ for some $$0< \sigma < 1$$. The parameter that is considered here is the spectral gap of the transition matrix. The main result is that this is greater than $$k/n$$, up to a polylogarithmic factor, with high probability over the random choice of the $$k$$ paths. The proof relies on the analysis of the spectral gap for a random walk on a similar random graph, where $$k$$ directed paths are formed which have length that is geometrically distributed and are joined as described above. Reviewer: Nikolaos Fountoulakis (Birmingham) Surface measures in infinite-dimensional spaces https://www.zbmath.org/1485.28002 2022-06-24T15:10:38.853281Z "Bogachev, Vladimir I." https://www.zbmath.org/authors/?q=ai:bogachev.vladimir-i For the entire collection see [Zbl 1388.28001]. Almost automorphic solutions for mean-field stochastic differential equations driven by fractional Brownian motion https://www.zbmath.org/1485.34147 2022-06-24T15:10:38.853281Z "Chen, Feng" https://www.zbmath.org/authors/?q=ai:chen.feng "Zhang, Xiaoying" https://www.zbmath.org/authors/?q=ai:zhang.xiaoying Summary: This paper concerns a class of mean field stochastic differential equations driven by fractional Brownian motion with Hurst parameter $$H\in(1/2,1)$$. The existence and uniqueness of almost automorphic solutions in distribution of mean field stochastic differential equations driven by fractional Brownian motion are established provided coefficients of equations satisfy some suitable conditions. Heat kernel of supercritical nonlocal operators with unbounded drifts https://www.zbmath.org/1485.35256 2022-06-24T15:10:38.853281Z "Menozzi, Stéphane" https://www.zbmath.org/authors/?q=ai:menozzi.stephane "Zhang, Xicheng" https://www.zbmath.org/authors/?q=ai:zhang.xicheng.1|zhang.xicheng Summary: Let $$\alpha\in (0,2)$$ and $$d\in\mathbb{N}$$. Consider the following stochastic differential equation (SDE) in $$\mathbb{R}^d$$: $\mathrm{d}X_t=b(t,X_t)\,\mathrm{d}t+a(t,X_{t-})\,\mathrm{d} L^{(\alpha )}_t,\quad X_0=x,$ where $$L^{(\alpha)}$$ is a $$d$$-dimensional rotationally invariant $$\alpha$$-stable process, $$b:\mathbb{R}_+\times \mathbb{R}^d\rightarrow\mathbb{R}^d$$ and $$a:\mathbb{R}_+\times \mathbb{R}^d\rightarrow\mathbb{R}^d\otimes\mathbb{R}^d$$ are Hölder continuous functions in space, with respective order $$\beta,\gamma\in (0,1)$$ such that $$(\beta\wedge\gamma)+\alpha>1$$, uniformly in $$t$$. Here $$b$$ may be unbounded. When $$a$$ is bounded and uniformly elliptic, we show that the unique solution $$X_t(x)$$ of the above SDE admits a continuous density, which enjoys sharp two-sided estimates. We also establish sharp upper-bound for the logarithmic derivative. In particular, we cover the whole \textit{supercritical} range $$\alpha\in (0,1)$$. Our proof is based on ad hoc parametrix expansions and probabilistic techniques. Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains https://www.zbmath.org/1485.35319 2022-06-24T15:10:38.853281Z "Giunti, Arianna" https://www.zbmath.org/authors/?q=ai:giunti.arianna "Höfer, Richard M." https://www.zbmath.org/authors/?q=ai:hofer.richard-m The authors prove a homogenization result, especially focusing on the pressure, for the steady incompressible Stokes equations $$-\Delta u_{\varepsilon }+\nabla p_{\varepsilon }=f$$, $$\nabla \cdot u_{\varepsilon }=0$$, posed in a domain $$D^{\varepsilon }$$, which is obtained by removing from a bounded set $$D\subset \mathbb{R}^{d}$$, $$d>2$$ a random number of small balls having random centers and radii: $$D^{\varepsilon }=D\setminus H^{\varepsilon }$$, with $$H^{\varepsilon }=\cup _{z_{i}\in \Phi \cap \frac{1}{ \varepsilon }D}B_{\varepsilon \frac{d}{d-2}\rho _{i}}(\varepsilon z_{i})$$, where $$\Phi$$ is a Poisson point process on $$\mathbb{R}^{d}$$ with homogeneous intensity rate $$\lambda >0$$, and the radii $$\{\rho _{i}\}_{z_{i}\in \Phi }\sqsubseteq \mathbb{R}_{+}$$ are identically and independently distributed unbounded random variables which satisfy $$\left\langle \rho ^{(d-2)+\beta }\right\rangle <+\infty$$ for some $$\beta >0$$, $$\left\langle \cdot \right\rangle$$ being the expectation under the probability measure on the radii $$\rho _{i}$$. The homogeneous Dirichlet boundary condition $$u_{\varepsilon }=0$$ is imposed in $$\partial D^{\varepsilon }$$. The source term $$f$$ is supposed to belong to $$H^{-1}(D; \mathbb{R}^{d})$$ and the above problem has a solution $$(u_{\varepsilon },p_{\varepsilon })$$ which belongs to $$H_{0}^{1}(D^{\varepsilon };\mathbb{R} ^{d})\times L_{0}^{2}(D^{\varepsilon };\mathbb{R})$$. The authors introduce the homogenized problem (Brinkman's equation): $$-\Delta u_{h}+\mu u_{h}+\nabla p_{h}=f$$, $$\nabla \cdot u_{h}=0$$, posed in $$D$$, where $$\mu =C_{d}\lambda \left\langle \rho ^{d-2}\right\rangle I$$, $$C_{d}>0$$ being a constant which only depends on the dimension $$d$$. The main result of the paper proves that for $$P$$-almost every $$\omega \in \Omega$$ there exists a family of sets $$E^{\varepsilon }\sqsubseteq \mathbb{R}^{d}$$ and a sequence $$r_{\varepsilon }\rightarrow 0$$ such that $$H^{\varepsilon }\sqsubseteq E^{\varepsilon }$$ and for $$\varepsilon \downarrow 0^{+}$$ $$Cap(E^{\varepsilon }\setminus H^{\varepsilon })\rightarrow 0$$, where $$Cap$$ denotes the harmonic capacity in $$\mathbb{R}^{d}$$. Further, the modification $$\widetilde{p} _{\varepsilon }$$ of the pressure defined as $$\widetilde{p}_{\varepsilon }=p_{\varepsilon }-\frac{1}{\left\vert D_{r_{\varepsilon }}\setminus E^{\varepsilon }\right\vert }\int_{D_{r_{\varepsilon }}\setminus E^{\varepsilon }}p_{\varepsilon }$$ in $$D_{r_{\varepsilon }}\setminus E^{\varepsilon }$$ and $$\widetilde{p}_{\varepsilon }=p_{\varepsilon }$$ in $$(D\setminus D_{r_{\varepsilon }})\cup E^{\varepsilon }$$, satisfies for all $$q<\frac{d}{d-1}$$ $$\widetilde{p}_{\varepsilon }\rightarrow p_{h}$$ in $$L_{0}^{q}(D;\mathbb{R})$$. Here $$D_{r}=\{x\in D:dist(x,\partial D)>r\}$$. The key tool for the proof is an estimate on the Bogovski operator in $$D\setminus E^{\varepsilon }$$. The authors also build appropriate test functions. Reviewer: Alain Brillard (Riedisheim) Controllability of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion with delay and Poisson jumps https://www.zbmath.org/1485.35370 2022-06-24T15:10:38.853281Z "Youssef, Benkabdi" https://www.zbmath.org/authors/?q=ai:youssef.benkabdi "El Hassan, Lakhel" https://www.zbmath.org/authors/?q=ai:el-hassan.lakhel Summary: In this paper the controllability of a class of impulsive neutral stochastic integro-differential systems driven by fractional Brownian motion and Poisson process in a separable Hilbert space with infinite delay is studied. The controllability result is obtained by using stochastic analysis and a fixed-point strategy. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result. On the liftability of expanding stationary measures https://www.zbmath.org/1485.37002 2022-06-24T15:10:38.853281Z "Alves, José F." https://www.zbmath.org/authors/?q=ai:alves.jose-ferreira "Dias, Carla L." https://www.zbmath.org/authors/?q=ai:dias.carla-l "Vilarinho, Helder" https://www.zbmath.org/authors/?q=ai:vilarinho.helder Quantifying the parameter dependent basin of the unsafe regime of asymmetric Lévy-noise-induced critical transitions https://www.zbmath.org/1485.37049 2022-06-24T15:10:38.853281Z "Ma, Jinzhong" https://www.zbmath.org/authors/?q=ai:ma.jinzhong "Xu, Yong" https://www.zbmath.org/authors/?q=ai:xu.yong.1|xu.yong.3 "Li, Yongge" https://www.zbmath.org/authors/?q=ai:li.yongge "Tian, Ruilan" https://www.zbmath.org/authors/?q=ai:tian.ruilan "Ma, Shaojuan" https://www.zbmath.org/authors/?q=ai:ma.shaojuan "Kurths, J." https://www.zbmath.org/authors/?q=ai:kurths.jurgen Summary: In real systems, the unpredictable jump changes of the random environment can induce the critical transitions (CTs) between two non-adjacent states, which are more catastrophic. Taking an asymmetric Lévy-noise-induced tri-stable model with desirable, sub-desirable, and undesirable states as a prototype class of real systems, a prediction of the noise-induced CTs from the desirable state directly to the undesirable one is carried out. We first calculate the region that the current state of the given model is absorbed into the undesirable state based on the escape probability, which is named as the absorbed region. Then, a new concept of the parameter dependent basin of the unsafe regime (PDBUR) under the asymmetric Lévy noise is introduced. It is an efficient tool for approximately quantifying the ranges of the parameters, where the noise-induced CTs from the desirable state directly to the undesirable one may occur. More importantly, it may provide theoretical guidance for us to adopt some measures to avert a noise-induced catastrophic CT. Real interpolation of martingale Orlicz Hardy spaces and BMO spaces https://www.zbmath.org/1485.46034 2022-06-24T15:10:38.853281Z "Long, Long" https://www.zbmath.org/authors/?q=ai:long.long "Weisz, Ferenc" https://www.zbmath.org/authors/?q=ai:weisz.ferenc "Xie, Guangheng" https://www.zbmath.org/authors/?q=ai:xie.guangheng Summary: In this article, the authors prove that the real interpolation spaces between martingale Orlicz Hardy spaces and martingale BMO spaces are martingale Orlicz-Lorentz Hardy spaces. Using sharp maximal functions, the authors also establish the characterizations of martingale Orlicz Hardy spaces. Homogenization of ferromagnetic energies on Poisson random sets in the plane https://www.zbmath.org/1485.49019 2022-06-24T15:10:38.853281Z "Braides, Andrea" https://www.zbmath.org/authors/?q=ai:braides.andrea "Piatnitski, Andrey" https://www.zbmath.org/authors/?q=ai:piatnitski.andrey-l The present paper studies a prototypical model of pair-interaction energies on Poisson random sets in the plane. These energies are a random version of nearest-neighbour ferromagnetic systems defined on Bravais lattices, whose overall behaviour is that of an interfacial energy. The analysis of ferromagnetic energies is relevant for numerical approximations and modeling issues in view of the possibility of lattice approximations for arbitrary interfacial energies makes, see [\textit{A. Braides} and \textit{L. Kreutz}, SIAM J. Math. Anal. 50, No. 2, 1485--1520 (2018; Zbl 1386.49017)]. The study of energies involving bulk and surface part can often be decoupled in the analysis of each part, which justifies the analysis of surface energies separately also in that context, see [\textit{F. Cagnetti} et al., Ann. Inst. Henri Poincaré, Anal. Non Linéaire 36, No. 4, 1035--1079 (2019; Zbl 1417.49010)] and the recent advances in the analysis and derivation of complex energies from discrete systems in [\textit{A. Bach} et al., SIAM J. Math. Anal. 52, No. 4, 3600--3665 (2020; Zbl 1446.49009)]. Discrete energies with randomness producing surface effects have been previously considered under various hypotheses. Results on regular lattices with random interactions comprise: random weak membrane models in [\textit{A. Braides} and \textit{A. Piatnitski}, Arch. Ration. Mech. Anal. 189, No. 2, 301--323 (2008; Zbl 1147.74039)], random ferromagnetic energies with positive coefficients in [\textit{A. Braides} and \textit{A. Piatnitski}, J. Funct. Anal. 264, No. 6, 1296--1328 (2013; Zbl 1270.35057)] and ferromagnetic energies with a random distribution of degenerate coefficients in [\textit{A. Braides} and \textit{A. Piatnitski}, J. Stat. Phys. 149, No. 5, 846--864 (2012; Zbl 1260.82043)]. The authors of the present paper prove that by scaling nearest-neighbour ferromagnetic energies defined on Poisson random sets in the plane one obtains an isotropic perimeter energy with a surface tension characterised by an asymptotic formula. Reviewer: Viktor Ohanyan (Erevan) Large deviations for random walks on free products of finitely generated groups https://www.zbmath.org/1485.60007 2022-06-24T15:10:38.853281Z "Corso, Emilio" https://www.zbmath.org/authors/?q=ai:corso.emilio This paper is concerned with the theory of random walks on a class of finitely generated groups, and specifically to the investigation of the asymptotic properties of the distribution of the renormalized distance from the origin. The main result establishes the existence of the large deviation principle, with a proper convex rate function, for the distribution of the renormalized distance from the origin of a random walk on a free product of finitely generated groups, under a non-degeneracy assumption on the semigroup $$\Gamma$$ generated by the support of a probability measure $$\mu$$. From this result, it derives the same principle for nearest-neighbour random walks on regular trees.\\ The paper starts with the presentation of some preliminaries on random walks on finitely generated groups and reviewing some standard terminology from the theory of large deviations. This serves the purpose of provide the notation to be used, clarify the nature of the assumption imposed on the semigroup $$\Gamma$$, and explains some general facts that are employed in the proof of the main result. At the end of the article, some ideas on possible generalizations of the main theorem are brought together, and some open questions and conjectures are formulated. Reviewer: Hernando Burgos-Soto (Toronto) Mean and minimum of independent random variables https://www.zbmath.org/1485.60011 2022-06-24T15:10:38.853281Z "Feldheim, Naomi Dvora" https://www.zbmath.org/authors/?q=ai:feldheim.naomi-dvora "Feldheim, Ohad Noy" https://www.zbmath.org/authors/?q=ai:feldheim.ohad-noy For any pair $$X,Y$$ of independent non-compactly supported random variables on $$[0, \infty)$$, this paper shows \begin{eqnarray*} \liminf_{n \rightarrow \infty} \mathbf{P}(min(X,Y)>m \;|\; X+Y>2m) = 0. \end{eqnarray*} Furthermore, the multi-variate and weighted generalizations of this result are proposed, which are proven under the additional assumption that the random variables are identically distributed. Reviewer: Ping Sun (Shenyang) Fourth moment bound and stationary Gaussian processes with positive correlation https://www.zbmath.org/1485.60026 2022-06-24T15:10:38.853281Z "Kim, Yoon Tae" https://www.zbmath.org/authors/?q=ai:kim.yoontae "Park, Hyun Suk" https://www.zbmath.org/authors/?q=ai:park.hyun-suk Summary: We develop a new technique for the proof of the fourth moment theorem on Wiener chaos to derive the bound in normal approximation of a random variable living a finite sum of Wiener chaos of a stationary Gaussian process with a positive correlaton. Thanks to newly developed techniques, an improved upper bound, expressed in terms of the fourth moment, will be obtained, compared with the one in [\textit{K. Es-Sebaiy} and \textit{F. G. Viens}, Stochastic Processes Appl. 129, No. 9, 3018--3054 (2019; Zbl 1422.60031)]. Our approach will be applied to the case where a random variable of functionals of Gaussian fields has a form of a power variation of a fractional Brownain motion and a polynomial variation of a fractional stationary Ornstein-Uhlenbeck process. The random walk penalised by its range in dimensions $$d\geqslant 3$$ https://www.zbmath.org/1485.60028 2022-06-24T15:10:38.853281Z "Berestycki, Nathanaël" https://www.zbmath.org/authors/?q=ai:berestycki.nathanael "Cerf, Raphaël" https://www.zbmath.org/authors/?q=ai:cerf.raphael The paper studies a self-attractive random walk. Its trajectories of length $$N$$ are penalised by factors proportional to $$exp(-|R_N|),$$ where $$R_N$$ is the set of sites visited by the walk. The main goal of the paper is to verify Bolthausen's conjecture [\textit{E. Bolthausen}, Ann. Probab. 22, No. 2, 875--918 (1994; Zbl 0819.60028)] for the case $$d>2$$. The authors prove that the range of the walk is close to a solid Euclidean ball of radius approximately $$\rho_dN^{1/(d+2)},$$ for some explicit constant $$\rho_d > 0.$$ Thus, the paper extends Bolthausen's estimates from the case $$d=2$$ to the general case $$d > 2,$$ which results in proving the conjecture. Also, a detailed discussion of related results and heuristics behind them is given. Reviewer: Andriy Olenko (Melbourne) Convergence of local supermartingales https://www.zbmath.org/1485.60039 2022-06-24T15:10:38.853281Z "Larsson, Martin" https://www.zbmath.org/authors/?q=ai:larsson.martin "Ruf, Johannes" https://www.zbmath.org/authors/?q=ai:ruf.johannes The theme of this paper is a characterisation of the event of the almost sure convergence of a local supermartingale. This is known through the Dambis-Dubins-Schwarz theorem which covers the case of continuous local supermartingales (the event of convergence coincides with that of having a finite quadratic variation). This paper considers local martingales which may not be continuous, but are restricted on a stochastic interval. In particular, the latter is defined as the interval between time 0 and a stopping time $$\tau$$ which is \textit{foretellable}, that is, it can be approximated from below by a non-decreasing sequence of stopping times. The main theorem gives a number of characterisations for the event of convergence within a measurable subset $$D$$ of such a local supermartingale $$(X_t)_{0\leq t < \tau}$$ as $$t\to \tau$$. This characterisation uses the notion of \textit{stationarily local integrability} on $$D$$. This property is defined through a non-decreasing sequence of stopping times $$(\rho_n)_{n\in \mathbb{N}}$$ such that the stopped process $$(X_t^{\rho_n})_{t\geq 0}$$ is uniformly bounded by an integrable random variable $$\Theta_n$$, for each $$n\in \mathbb{N}$$ and moreover $$D$$ contains the event that one of these stopping times exceeds $$\tau$$. Reviewer: Nikolaos Fountoulakis (Birmingham) On discrete-time self-similar processes with stationary increments https://www.zbmath.org/1485.60040 2022-06-24T15:10:38.853281Z "Shen, Yi" https://www.zbmath.org/authors/?q=ai:shen.yi|shen.yi.1|shen.yi.3|shen.yi.2|shen.yi.4 "Zhang, Zhenyuan" https://www.zbmath.org/authors/?q=ai:zhang.zhenyuan Based on authors' abstract: This paper studies the self-similar processes with stationary increments in a discrete-time setting. It is shown that the scaling function of such a process may not take the form of a power function. Its scaling function can belong to one of three types, among which one type is degenerate, one type has a continuous-time counterpart, while the other type is new and unique for the discrete-time setting. The paper focus on this last type of processes, construct two classes of examples, and prove a special spectral representation result for the processes of this type. The paper also derives basic properties of discrete-time self-similar processes with stationary increments of different types. Reviewer: Pedro A. Morettin (São Paulo) On the Besov regularity of the bifractional Brownian motion https://www.zbmath.org/1485.60041 2022-06-24T15:10:38.853281Z "Boufoussi, Brahim" https://www.zbmath.org/authors/?q=ai:boufoussi.brahim "Nachit, Yassine" https://www.zbmath.org/authors/?q=ai:nachit.yassine Summary: Our aim is to improve Hölder continuity results for the bifractional Brownian motion (bBm) $$(B^{\alpha,\beta}(t))_{t\in [0,1]}$$ with $$0<\alpha <1$$ and $$0<\beta\leqslant 1$$. We prove that almost all paths of the bBm belong to (resp. do not belong to) the Besov spaces $$\mathbf{Bes}(\alpha \beta,p)$$ (resp. $$\mathbf{bes}(\alpha \beta,p))$$ for any $$\frac{1}{\alpha \beta}<p<\infty$$, where $$\mathbf{bes}(\alpha \beta,p)$$ is a separable subspace of $$\mathbf{Bes}(\alpha \beta,p)$$. We also show similar regularity results in the Besov-Orlicz space $$\mathbf{Bes}(\alpha \beta, M_2)$$ with $$M_2 (x)=e^{x^2}-1$$. We conclude by proving the Ito-Nisio theorem for the bBm with $$\alpha \beta>1/2$$ in the Hölder spaces $$\mathcal{C}^{\gamma}$$ with $$\gamma <\alpha \beta$$. Modelling Lévy space-time white noises https://www.zbmath.org/1485.60042 2022-06-24T15:10:38.853281Z "Griffiths, Matthew" https://www.zbmath.org/authors/?q=ai:griffiths.matthew "Riedle, Markus" https://www.zbmath.org/authors/?q=ai:riedle.markus The paper studies cylindrical Lévy processes and Lévy space-time white noises, and considers their embeddings in the space of general and tempered Schwartz distributions. It proves that Lévy space-time white noises form an entire sub-class of cylindrical Lévy processes. Necessary and sufficient conditions for the embedding are obtained. The paper provides an exact characterisation of the subclass of cylindrical Lévy processes which correspond to Lévy-valued random measures. The elements of this class are completely determined by their characteristic functions. Finally, a representation of Lévy space-time white noises as weak derivatives of Lévy additive sheets is given. The introduction and detailed bibliography demonstrate how the these findings generalise known results and models. Reviewer: Andriy Olenko (Melbourne) Fractional Ornstein-Uhlenbeck process with stochastic forcing, and its applications https://www.zbmath.org/1485.60043 2022-06-24T15:10:38.853281Z "Ascione, Giacomo" https://www.zbmath.org/authors/?q=ai:ascione.giacomo "Mishura, Yuliya" https://www.zbmath.org/authors/?q=ai:mishura.yuliya-s "Pirozzi, Enrica" https://www.zbmath.org/authors/?q=ai:pirozzi.enrica The authors introduce a fractional Ornstein-Uhlenbeck process involving a stochastic forcing term in the drift as a solution of a linear stochastic differential equation driven by a fractional Brownian motion with Hurst index $$H.$$ They derive the mean and the covariance function for such processes and study their asymptotic behaviour as $$H\rightarrow 0$$ and as $$H\rightarrow 1.$$ Applications of this process in neuronal modeling are investigated. Reviewer: B. L. S. Prakasa Rao (Hyderabad) A note on inference for the mixed fractional Ornstein-Uhlenbeck process with drift https://www.zbmath.org/1485.60044 2022-06-24T15:10:38.853281Z "Cai, Chunhao" https://www.zbmath.org/authors/?q=ai:cai.chunhao "Zhang, Min" https://www.zbmath.org/authors/?q=ai:zhang.min.2|zhang.min.5|zhang.min|zhang.min.6|zhang.min.3|zhang.min.7|zhang.min.4|zhang.min.1 Summary: This paper is devoted to the controlled drift estimation of the mixed fractional Ornstein-Uhlenbeck process. We will consider two models: one is the optimal input where we will find the controlled function which maximize the Fisher information for the unknown parameter and the other one with a constant as the controlled function. Large sample asymptotical properties of the Maximum Likelihood Estimator (MLE) is deduced using the Laplace transform computations or the Cameron-Martin formula with extra part from [\textit{P. Chigansky} and \textit{M. Kleptsyna}, Theory Probab. Appl. 63, No. 3, 408--425 (2019; Zbl 1411.62053)]. As a a supplement of [loc. cit.] we will also prove that the MLE is strongly consistent. Regularity of fractional stochastic convolution and its application to fractional stochastic chaotic systems https://www.zbmath.org/1485.60045 2022-06-24T15:10:38.853281Z "Huang, Xiuqi" https://www.zbmath.org/authors/?q=ai:huang.xiuqi "Wang, Xiangjun" https://www.zbmath.org/authors/?q=ai:wang.xiangjun Summary: The current paper is devoted to the regularity of Caputo-type fractional Onstein-Ulenbeck processes with fractional Brownian motion, and it is applied to establish the existence and uniqueness of the mild solution for Caputo-type fractional Rössler equation and fractional Chen equation with fractional Brownian motion. Some numerical simulations and examples are provided to support the theoretical results. Two-sided optimal stopping for Lévy processes https://www.zbmath.org/1485.60046 2022-06-24T15:10:38.853281Z "Mordecki, Ernesto" https://www.zbmath.org/authors/?q=ai:mordecki.ernesto "Eguren, Facundo Oliú" https://www.zbmath.org/authors/?q=ai:eguren.facundo-oliu The authors study the infinite horizon optimal stopping problems for a Lévy processes with a two-sided reward function. The purpose of the paper is to obtain a verification theorem for the optimal stopping problem of a Lévy process in the two sided case, through the sum of two averaging functions. A two-sided verification theorem is presented in terms of the overall supremum and the overall infimum of the process. Also, a result how to compute the angle of the value function at the optimal thresholds of the stopping region is given. Some attention is paid to the natural necessary conditions for smooth pasting, that depend on the exponential moments of the process and the behaviour of the averaging function. These conditions can be applied both to one-sided problems and to the two sided problems considered in the present paper. Then the authors provide a simple example that seems not possible to be solved with the previously known techniques. Namely, the optimal stopping problem of a compound Poisson process with two-sided exponential jumps (no Gaussian component) and a two-sided payoff function is solved. In this example, the smooth-pasting condition does not hold. Reviewer: Yuliya S. Mishura (Kyïv) Realized cumulants for martingales https://www.zbmath.org/1485.60047 2022-06-24T15:10:38.853281Z "Fukasawa, Masaaki" https://www.zbmath.org/authors/?q=ai:fukasawa.masaaki "Matsushita, Kazuki" https://www.zbmath.org/authors/?q=ai:matsushita.kazuki In the present paper, authors do develop a cumulants' extraction of high frequency data, which usually appear in financial markets. This paper focus on arithmetic techniques for moments' calculation, which may applied on forecasting values of such data. Reviewer: Christos E. Kountzakis (Karlovassi) Functional advantages of Lévy walks emerging near a critical point https://www.zbmath.org/1485.60048 2022-06-24T15:10:38.853281Z "Abe, Masato S." https://www.zbmath.org/authors/?q=ai:abe.masato-s Summary: A special class of random walks, so-called Lévy walks, has been observed in a variety of organisms ranging from cells, insects, fishes, and birds to mammals, including humans. Although their prevalence is considered to be a consequence of natural selection for higher search efficiency, some findings suggest that Lévy walks might also be epiphenomena that arise from interactions with the environment. Therefore, why they are common in biological movements remains an open question. Based on some evidence that Lévy walks are spontaneously generated in the brain and the fact that power-law distributions in Lévy walks can emerge at a critical point, we hypothesized that the advantages of Lévy walks might be enhanced by criticality. However, the functional advantages of Lévy walks are poorly understood. Here, we modeled nonlinear systems for the generation of locomotion and showed that Lévy walks emerging near a critical point had optimal dynamic ranges for coding information. This discovery suggested that Lévy walks could change movement trajectories based on the magnitude of environmental stimuli. We then showed that the high flexibility of Lévy walks enabled switching exploitation/exploration based on the nature of external cues. Finally, we analyzed the movement trajectories of freely moving Drosophila larvae and showed empirically that the Lévy walks may emerge near a critical point and have large dynamic range and high flexibility. Our results suggest that the commonly observed Lévy walks emerge near a critical point and could be explained on the basis of these functional advantages. Limit theorems for additive functionals of continuous time random walks https://www.zbmath.org/1485.60049 2022-06-24T15:10:38.853281Z "Kondratiev, Yuri" https://www.zbmath.org/authors/?q=ai:kondratiev.yuri-g "Mishura, Yuliya" https://www.zbmath.org/authors/?q=ai:mishura.yuliya-s "Shevchenko, Georgiy" https://www.zbmath.org/authors/?q=ai:shevchenko.georgiy-m Let $$(X_t)_{t\geq 0}$$ be a continuous-time random walk in which the inter-arrival times $$(\theta_i)_{i\geq 1}$$ are iid and integrable, and the distribution of iid jumps $$(\xi_k)_{k\geq 1}$$ is centered and spread-out, belongs to the domain of attraction of an $$\alpha$$-stable distribution $$\mu_\alpha$$, say, $$\alpha\in (1,2]$$ and satisfies an additional condition. Assuming that $$f$$ satisfies a suitable integrability condition the authors prove that finite-dimensional distributions of $$(\int_0^{tu}f(X_s)\mathrm{d}s)_{u\geq 0}$$ converge weakly as $$t\to\infty$$ to a multiple of a symmetric local time at zero of $$Z_\alpha$$, where $$Z_\alpha$$ is an $$\alpha$$-stable Lévy process with the distribution of $$Z_\alpha(1)$$ being $$\mu_\alpha$$. A similar result is also obtained for a more complicated model in which the inter-arrival time depends on the current position of the walking particle. Namely, the original inter-arrival time $$\theta_i$$ is replaced with $$\theta_i/\Lambda(\xi_1+\ldots+\xi_i)$$, where $$\Lambda$$ is either deterministic or random and independent of everything else. Particular attention is paid to the case in which $$\Lambda$$ is a Poisson-shot noise potential. Reviewer: Alexander Iksanov (Kiev) A new proof of the stick-breaking representation of Dirichlet processes https://www.zbmath.org/1485.60050 2022-06-24T15:10:38.853281Z "Lee, Jaeyong" https://www.zbmath.org/authors/?q=ai:lee.jaeyong "MacEachern, Steven N." https://www.zbmath.org/authors/?q=ai:maceachern.steven-n Summary: The stick-breaking representation is one of the fundamental properties of the Dirichlet process. It represents the random probability measure as a discrete random sum whose weights and atoms are formed by independent and identically distributed sequences of beta variates and draws from the normalized base measure of the Dirichlet process parameter. It is used extensively in posterior simulation for statistical models with Dirichlet processes. The original proof of \textit{J. Sethuraman} [Stat. Sin. 4, No. 2, 639--650 (1994; Zbl 0823.62007)] relies on an indirect distributional equation and does not encourage an intuitive understanding of the property. In this paper, we give a new proof of the stick-breaking representation of the Dirichlet process that provides an intuitive understanding of the theorem. The proof is based on the posterior distribution and self-similarity properties of the Dirichlet process. Stochastic elliptic operators defined by non-Gaussian random fields with uncertain spectrum https://www.zbmath.org/1485.60051 2022-06-24T15:10:38.853281Z "Soize, C." https://www.zbmath.org/authors/?q=ai:soize.christian The author studies a class of non-Gaussian positive-definite matrix-valued homogeneous random fields. The stochastic homogenization of a 3D-linear anisotropic elastic random medium is considered. The elasticity field is modeled by a non-Gaussian fourth-order tensor-valued homogeneous random field. A new model based on a parametrization of the spectral measure is proposed. For this model the stochastic elliptic boundary value problem in a bounded domain of the 3D-space is investigated. Reviewer: Andriy Olenko (Melbourne) High-dimensional inference using the extremal skew-$$t$$ process https://www.zbmath.org/1485.60052 2022-06-24T15:10:38.853281Z "Beranger, B." https://www.zbmath.org/authors/?q=ai:beranger.boris "Stephenson, A. G." https://www.zbmath.org/authors/?q=ai:stephenson.alec-g "Sisson, S. A." https://www.zbmath.org/authors/?q=ai:sisson.scott-a Authors' abstract: Max-stable processes are a popular tool for the study of environmental extremes, and the extremal skew-$$t$$ process is a general model that allows for a flexible extremal dependence structure. For inference on max-stable processes with high-dimensional data, exact likelihood-based estimation is computationally intractable. Composite likelihoods, using lower dimensional components, and Stephenson-Tawn likelihoods, using occurrence times of maxima, are both attractive methods to circumvent this issue for moderate dimensions. In this article we establish the theoretical formulae for simulations of and inference for the extremal skew-$$t$$ process. We also incorporate the Stephenson-Tawn concept into the composite likelihood framework, giving greater statistical and computational efficiency for higher-order composite likelihoods. We compare 2-way (pairwise), 3-way (triplewise), 4-way, 5-way and 10-way composite likelihoods for models of up to 100 dimensions. Furthermore, we propose cdf approximations for the Stephenson-Tawn likelihood function, leading to large computational gains, and enabling accurate fitting of models in large dimensions in only a few minutes. We illustrate our methodology with an application to a 90-dimensional temperature dataset from Melbourne, Australia. Reviewer: Edward Omey (Brussel) Fuzzy stochastic differential equations driven by fractional Brownian motion https://www.zbmath.org/1485.60054 2022-06-24T15:10:38.853281Z "Jafari, Hossein" https://www.zbmath.org/authors/?q=ai:jafari.hossein.1|jafari.hossein "Malinowski, Marek T." https://www.zbmath.org/authors/?q=ai:malinowski.marek-t "Ebadi, M. J." https://www.zbmath.org/authors/?q=ai:ebadi.mohammad-javad Summary: In this paper, we consider fuzzy stochastic differential equations (FSDEs) driven by fractional Brownian motion (fBm). These equations can be applied in hybrid real-world systems, including randomness, fuzziness and long-range dependence. Under some assumptions on the coefficients, we follow an approximation method to the fractional stochastic integral to study the existence and uniqueness of the solutions. As an example, in financial models, we obtain the solution for an equation with linear coefficients. Periodic measures of impulsive stochastic differential equations https://www.zbmath.org/1485.60055 2022-06-24T15:10:38.853281Z "Li, Dingshi" https://www.zbmath.org/authors/?q=ai:li.dingshi "Lin, Yusen" https://www.zbmath.org/authors/?q=ai:lin.yusen Summary: This paper is concerned with the periodic stochastic differential equations with nonlinear impulses. By using the properties of periodic Markov processes, the existence of periodic measures for the impulsive stochastic equations is established. As applications, we study the existence of periodic measures of impulsive periodic stochastic logistic equations and impulsive periodic stochastic neural networks, respectively. On boundedness and convergence of solutions for neutral stochastic functional differential equations driven by G-Brownian motion https://www.zbmath.org/1485.60064 2022-06-24T15:10:38.853281Z "Faizullah, Faiz" https://www.zbmath.org/authors/?q=ai:faizullah.faiz Summary: The current article presents the study of neutral stochastic functional differential equations driven by G-Brownian motion in the phase space $$C_q((-\infty ,0];\mathbb{R}^n)$$. The mean-square boundedness of solutions has been derived. The convergence of solutions with different initial data has been investigated. The boundedness and convergence of solution maps have been obtained. In addition, the $$L^2_G$$ and exponential estimates of solutions have been determined. On reflection with two-sided jumps https://www.zbmath.org/1485.60065 2022-06-24T15:10:38.853281Z "Jarni, Imane" https://www.zbmath.org/authors/?q=ai:jarni.imane "Ouknine, Youssef" https://www.zbmath.org/authors/?q=ai:ouknine.youssef The authors study a Skorokhod problem with jumps, reflected in the half line $$\mathbb R_+$$ and associated to a right limited and left limited function. Existence and uniqueness of solutions is discussed. The findings are applied to reflected stochastic differential equations driven by optional semimartingales. Reviewer: Henri Schurz (Carbondale) Construction and heat kernel estimates of general stable-like Markov processes https://www.zbmath.org/1485.60072 2022-06-24T15:10:38.853281Z "Knopova, Victoria" https://www.zbmath.org/authors/?q=ai:knopova.victoria-p "Kulik, Alexei" https://www.zbmath.org/authors/?q=ai:kulik.alexey-m "Schilling, René L." https://www.zbmath.org/authors/?q=ai:schilling.rene-leander A Lévy-type model is called essentially singular if the values of the $$x$$-dependent jump (Lévy) kernel cannot be dominated by a single reference measure; in the stable like setting this means that the distribution of the jump directions strongly varies from place to place. The analysis of such models encounters conceptual difficulties. Their analysis of stable-like processes does not require that the gradient term is dominated, and it works for essentially singular models. The main theorem of the paper shows that the first (principal) part in the decomposition for the transition density $$p_t(x; y)$$ can be represented with the help of a scaled version of an $$\alpha(x)$$-stable density where they make a drift correction of the starting point $$x$$ by moving it along the mollified drift vector field to the position. Reviewer: Rózsa Horváth-Bokor (Budakalász) Transition densities of spectrally positive Lévy processes https://www.zbmath.org/1485.60073 2022-06-24T15:10:38.853281Z "Leżaj, Łukasz" https://www.zbmath.org/authors/?q=ai:lezaj.lukasz The author considers one-dimensional Lévy processes of unbounded variation with only positive jumps. Just under the assumption that the second derivative of the Laplace exponent satisfies a weak lower scaling property at infinity, he proves that the Lévy process has a density at every time $$t$$ and computes its asymptotic behavior. In the special case of Lévy processes without Gaussian component and under some additional assumptions on the Laplace exponent, the author obtains sharp upper and lower estimates on the density. Reviewer: Artem Sapozhnikov (Leipzig) On the use of Markovian stick-breaking priors https://www.zbmath.org/1485.60074 2022-06-24T15:10:38.853281Z "Lippitt, William" https://www.zbmath.org/authors/?q=ai:lippitt.william "Sethuraman, Sunder" https://www.zbmath.org/authors/?q=ai:sethuraman.sunder Summary: Recently, a Markovian stick-breaking'' process which generalizes the Dirichlet process $$(\mu,\theta)$$ with respect to a discrete base space $$\mathfrak{X}$$ was introduced. In particular, a sample form from the Markovian stick-breaking'' processs may be represented in stick-breaking form $$\sum_{i\geq 1}P_i\delta_{T_i}$$ where $$\{T_i\}$$ is a stationary, irreducible Markov chain on $$\mathfrak{X}$$ with stationary distribution $$\mu$$, instead of i.i.d. $$\{T_i\}$$ each distributed as $$\mu$$ as in the Dirichlet case, and $$\{P_i\}$$ is a GEM $$(\theta)$$ residual allocation sequence. Although the previous motivation was to relate these Markovian stick-breaking processes to empirical distributional limits of types of simulated annealing chains, these processes may also be thought of as a class of priors in statistical problems. The aim of this work in this context is to identify the posterior distribution and to explore the role of the Markovian structure of $$\{T_i\}$$ in some inference test cases. For the entire collection see [Zbl 07455846]. A phase transition in the coming down from infinity of simple exchangeable fragmentation-coagulation processes https://www.zbmath.org/1485.60082 2022-06-24T15:10:38.853281Z "Foucart, Clément" https://www.zbmath.org/authors/?q=ai:foucart.clement Summary: We consider the class of exchangeable fragmentation-coagulation (EFC) processes where coagulations are multiple and not simultaneous, as in a $$\Lambda$$-coalescent, and fragmentation dislocates at a finite rate an individual block into sub-blocks of infinite size. We call these partition-valued processes simple EFC processes, and study the question whether such a process, when started with infinitely many blocks, can visit partitions with a finite number of blocks or not. When this occurs, one says that the process comes down from infinity. We introduce two sharp parameters $$\theta_{\star} \leq \theta^{\star}\in [0,\infty]$$, so that if $$\theta^{\star} < 1$$, the process comes down from infinity and if $$\theta_{\star} >1$$, then it stays infinite. We illustrate our result with regularly varying coagulation and fragmentation measures. In this case, the parameters $$\theta^{\star}, \theta_{\star}$$ coincide and are explicit. Gaussian determinantal processes: a new model for directionality in data https://www.zbmath.org/1485.62074 2022-06-24T15:10:38.853281Z "Ghosh, Subhroshekhar" https://www.zbmath.org/authors/?q=ai:ghosh.subhroshekhar "Rigollet, Philippe" https://www.zbmath.org/authors/?q=ai:rigollet.philippe Summary: Determinantal point processes (DPPs) have recently become popular tools for modeling the phenomenon of negative dependence, or repulsion, in data. However, our understanding of an analogue of a classical parametric statistical theory is rather limited for this class of models. In this work, we investigate a parametric family of Gaussian DPPs with a clearly interpretable effect of parametric modulation on the observed points. We show that parameter modulation impacts the observed points by introducing directionality in their repulsion structure, and the principal directions correspond to the directions of maximal (i.e., the most long-ranged) dependency. This model readily yields a viable alternative to principal component analysis (PCA) as a dimension reduction tool that favors directions along which the data are most spread out. This methodological contribution is complemented by a statistical analysis of a spiked model similar to that employed for covariance matrices as a framework to study PCA. These theoretical investigations unveil intriguing questions for further examination in random matrix theory, stochastic geometry, and related topics. Minimum risk point estimation of Gini index https://www.zbmath.org/1485.62109 2022-06-24T15:10:38.853281Z "De, Shyamal K." https://www.zbmath.org/authors/?q=ai:de.shyamal-krishna "Chattopadhyay, Bhargab" https://www.zbmath.org/authors/?q=ai:chattopadhyay.bhargab Summary: This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost at the same time. In this article, a purely sequential procedure is proposed which provides an estimate of the sample size required to achieve a sufficiently smaller estimation error and lower sampling cost. Characteristics of the purely sequential procedure are examined and asymptotic optimality properties are proved without assuming any specific distribution of the data. Performance of our method is examined through extensive simulation study. Applying of the extreme value theory for determining extreme claims in the automobile insurance sector: case of a China car insurance https://www.zbmath.org/1485.62145 2022-06-24T15:10:38.853281Z "Diawara, Daouda" https://www.zbmath.org/authors/?q=ai:diawara.daouda "Kane, Ladji" https://www.zbmath.org/authors/?q=ai:kane.ladji "Dembele, Soumaila" https://www.zbmath.org/authors/?q=ai:dembele.soumaila "Lo, Gane Samb" https://www.zbmath.org/authors/?q=ai:lo.gane-samb (no abstract) Varying coefficient models and design choice for Bayes linear emulation of complex computer models with limited model evaluations https://www.zbmath.org/1485.62169 2022-06-24T15:10:38.853281Z "Wilson, Amy L." https://www.zbmath.org/authors/?q=ai:wilson.amy-l "Goldstein, Michael" https://www.zbmath.org/authors/?q=ai:goldstein.michael-m|goldstein.michael.1|goldstein.michael.2 "Dent, Chris J." https://www.zbmath.org/authors/?q=ai:dent.chris-j Random walks with multiple step lengths https://www.zbmath.org/1485.68243 2022-06-24T15:10:38.853281Z "Boczkowski, Lucas" https://www.zbmath.org/authors/?q=ai:boczkowski.lucas "Guinard, Brieuc" https://www.zbmath.org/authors/?q=ai:guinard.brieuc "Korman, Amos" https://www.zbmath.org/authors/?q=ai:korman.amos "Lotker, Zvi" https://www.zbmath.org/authors/?q=ai:lotker.zvi "Renault, Marc" https://www.zbmath.org/authors/?q=ai:renault.marc-s|renault.marc-p Summary: In nature, search processes that use randomly oriented steps of different lengths have been observed at both the microscopic and the macroscopic scales. Physicists have analyzed in depth two such processes on grid topologies: intermittent search, which uses two step lengths, and Lévy walk, which uses many. Taking a computational perspective, this paper considers the number of distinct step lengths $$k$$ as a complexity measure of the considered process. Our goal is to understand what is the optimal achievable time needed to cover the whole terrain, for any given value of $$k$$. Attention is restricted to dimension one, since on higher dimensions, the simple random walk already displays a quasi linear cover time. We say $$X$$ is a $$k$$-intermittent search on the one dimensional $$n$$-node cycle if there exists a probability distribution $$\mathbf{p}=(p_i)_{i=1}^k$$, and integers $$L_1,L_2,\ldots, L_k$$, such that on each step $$X$$ makes a jump $$\pm L_i$$ with probability $$p_i$$, where the direction of the jump $$(+$$ or $$-)$$ is chosen independently with probability 1/2. When performing a jump of length $$L_i$$, the process consumes time $$L_i$$, and is only considered to visit the last point reached by the jump (and not any other intermediate nodes). This assumption is consistent with biological evidence, in which entities do not search while moving ballistically. We provide upper and lower bounds for the cover time achievable by $$k$$-intermittent searches for any integer $$k$$. In particular, we prove that in order to reduce the cover time $${\varTheta}(n^2)$$ of a simple random walk to linear in $$n$$ up to logarithmic factors, roughly $$\frac{\log n}{\log\log n}$$ step lengths are both necessary and sufficient, and we provide an example where the lengths form an exponential sequence. In addition, inspired by the notion of intermittent search, we introduce the Walk or Probe Problem, which can be defined with respect to arbitrary graphs. Here, it is assumed that querying (probing) a node takes significantly more time than moving to a random neighbor. Hence, to efficiently probe all nodes, the goal is to balance the time spent walking randomly and the time spent probing. We provide preliminary results for connected graphs and regular graphs. For the entire collection see [Zbl 1428.68007]. Measuring parity violation in the stochastic gravitational wave background with the LISA-Taiji network https://www.zbmath.org/1485.83015 2022-06-24T15:10:38.853281Z "Orlando, Giorgio" https://www.zbmath.org/authors/?q=ai:orlando.giorgio "Pieroni, Mauro" https://www.zbmath.org/authors/?q=ai:pieroni.mauro "Ricciardone, Angelo" https://www.zbmath.org/authors/?q=ai:ricciardone.angelo Detecting the relativistic bispectrum in 21cm intensity maps https://www.zbmath.org/1485.83027 2022-06-24T15:10:38.853281Z "Jolicoeur, Sheean" https://www.zbmath.org/authors/?q=ai:jolicoeur.sheean "Maartens, Roy" https://www.zbmath.org/authors/?q=ai:maartens.roy "De Weerd, Eline M." https://www.zbmath.org/authors/?q=ai:de-weerd.eline-m "Umeh, Obinna" https://www.zbmath.org/authors/?q=ai:umeh.obinna "Clarkson, Chris" https://www.zbmath.org/authors/?q=ai:clarkson.chris-a "Camera, Stefano" https://www.zbmath.org/authors/?q=ai:camera.stefano The integrated angular bispectrum of weak lensing https://www.zbmath.org/1485.83028 2022-06-24T15:10:38.853281Z "Jung, Gabriel" https://www.zbmath.org/authors/?q=ai:jung.gabriel "Namikawa, Toshiya" https://www.zbmath.org/authors/?q=ai:namikawa.toshiya "Liguori, Michele" https://www.zbmath.org/authors/?q=ai:liguori.michele "Munshi, Dipak" https://www.zbmath.org/authors/?q=ai:munshi.dipak "Heavens, Alan" https://www.zbmath.org/authors/?q=ai:heavens.alan-f On rotating black holes in DHOST theories https://www.zbmath.org/1485.83059 2022-06-24T15:10:38.853281Z "Achour, Jibril Ben" https://www.zbmath.org/authors/?q=ai:achour.jibril-ben "Liu, Hongguang" https://www.zbmath.org/authors/?q=ai:liu.hongguang "Motohashi, Hayato" https://www.zbmath.org/authors/?q=ai:motohashi.hayato "Mukohyama, Shinji" https://www.zbmath.org/authors/?q=ai:mukohyama.shinji "Noui, Karim" https://www.zbmath.org/authors/?q=ai:noui.karim Comparing multi-field primordial feature models with the Planck data https://www.zbmath.org/1485.83124 2022-06-24T15:10:38.853281Z "Braglia, Matteo" https://www.zbmath.org/authors/?q=ai:braglia.matteo "Chen, Xingang" https://www.zbmath.org/authors/?q=ai:chen.xingang "Hazra, Dhiraj Kumar" https://www.zbmath.org/authors/?q=ai:hazra.dhiraj-kumar Filtered pseudo-scalar dark matter and gravitational waves from first order phase transition https://www.zbmath.org/1485.83129 2022-06-24T15:10:38.853281Z "Chao, Wei" https://www.zbmath.org/authors/?q=ai:chao.wei "Li, Xiu-Fei" https://www.zbmath.org/authors/?q=ai:li.xiu-fei "Wang, Lei" https://www.zbmath.org/authors/?q=ai:wang.lei.11|wang.lei.17|wang.lei.19|wang.lei.6|wang.lei.18|wang.lei.16|wang.lei.14|wang.lei|wang.lei.8|wang.lei.15|wang.lei.9|wang.lei.5|wang.lei.4|wang.lei.7 Cross-correlations as a diagnostic tool for primordial gravitational waves https://www.zbmath.org/1485.83160 2022-06-24T15:10:38.853281Z "Malhotra, Ameek" https://www.zbmath.org/authors/?q=ai:malhotra.ameek "Dimastrogiovanni, Ema" https://www.zbmath.org/authors/?q=ai:dimastrogiovanni.ema "Fasiello, Matteo" https://www.zbmath.org/authors/?q=ai:fasiello.matteo "Shiraishi, Maresuke" https://www.zbmath.org/authors/?q=ai:shiraishi.maresuke Influence of cosmological expansion in local experiments https://www.zbmath.org/1485.83182 2022-06-24T15:10:38.853281Z "Spengler, Felix" https://www.zbmath.org/authors/?q=ai:spengler.felix "Belenchia, Alessio" https://www.zbmath.org/authors/?q=ai:belenchia.alessio "Rätzel, Dennis" https://www.zbmath.org/authors/?q=ai:ratzel.dennis "Braun, Daniel" https://www.zbmath.org/authors/?q=ai:braun.daniel|braun.daniel-a Local primordial non-Gaussianity in the relativistic galaxy bispectrum https://www.zbmath.org/1485.85002 2022-06-24T15:10:38.853281Z "Maartens, Roy" https://www.zbmath.org/authors/?q=ai:maartens.roy "Jolicoeur, Sheean" https://www.zbmath.org/authors/?q=ai:jolicoeur.sheean "Umeh, Obinna" https://www.zbmath.org/authors/?q=ai:umeh.obinna "De Weerd, Eline M." https://www.zbmath.org/authors/?q=ai:de-weerd.eline-m "Clarkson, Chris" https://www.zbmath.org/authors/?q=ai:clarkson.chris-a Responses of halo occupation distributions: a new ingredient in the halo model \& the impact on galaxy bias https://www.zbmath.org/1485.85022 2022-06-24T15:10:38.853281Z "Voivodic, Rodrigo" https://www.zbmath.org/authors/?q=ai:voivodic.rodrigo "Barreira, Alexandre" https://www.zbmath.org/authors/?q=ai:barreira.alexandre Measuring the primordial gravitational wave background in the presence of other stochastic signals https://www.zbmath.org/1485.85027 2022-06-24T15:10:38.853281Z "Poletti, D." https://www.zbmath.org/authors/?q=ai:poletti.dario|poletti.damiano Fuzzy testing of operating performance index based on confidence intervals https://www.zbmath.org/1485.90021 2022-06-24T15:10:38.853281Z "Chen, Kuen-Suan" https://www.zbmath.org/authors/?q=ai:chen.kuensuan Summary: The operating performance index (OPI) was developed by \textit{K.-S. Chen} and \textit{C.-M. Yang} [J. Comput. Appl. Math. 343, 737--747 (2018; Zbl 1457.90053)] from the Six Sigma process quality index. The fact that OPIs include unknown parameters means that they must be formulated using estimates based on sample data. Unfortunately, cost and effectiveness considerations in practice have led to sample size limitation and measurement uncertainty. In this study, we sought to enhance testing accuracy and overcome the uncertainties in measurement by applying confidence intervals of OPI to derive a fuzzy number and membership function for OPI. We developed a one-tailed fuzzy test method to determine whether performance reaches the required level. We also developed a two-tailed fuzzy testing method based on two OPIs to serve as a verification model for the effectiveness of improvement measures. Both fuzzy testing methods are proposed based on confidence intervals of the indices to reduce the risk of misjudgment caused by sampling errors and enhance testing accuracy. How to detect a salami slicer: a stochastic controller-and-stopper game with unknown competition https://www.zbmath.org/1485.91016 2022-06-24T15:10:38.853281Z "Ekström, Erik" https://www.zbmath.org/authors/?q=ai:ekstrom.erik "Lindensjö, Kristoffer" https://www.zbmath.org/authors/?q=ai:lindensjo.kristoffer "Olofsson, Marcus" https://www.zbmath.org/authors/?q=ai:olofsson.marcus Iterated prisoner's dilemma among mobile agents performing 2D random walk https://www.zbmath.org/1485.91022 2022-06-24T15:10:38.853281Z "Hižak, Jurica" https://www.zbmath.org/authors/?q=ai:hizak.jurica Summary: When iterated prisoner's dilemma takes place on a two-dimensional plane among mobile agents, the course of the game slightly differs from that one in a well-mixed population. In this paper we present a detailed derivation of the expected number of encounters required for tit-for-tat strategy to get even with always-defect strategy in a Brownian-like population. It will be shown that in such an environment tit-for-tat can perform better than in a well-mixed population. Making Tweedie's compound Poisson model more accessible https://www.zbmath.org/1485.91208 2022-06-24T15:10:38.853281Z "Delong, Łukasz" https://www.zbmath.org/authors/?q=ai:delong.lukasz "Lindholm, Mathias" https://www.zbmath.org/authors/?q=ai:lindholm.mathias "Wüthrich, Mario V." https://www.zbmath.org/authors/?q=ai:wuthrich.mario-valentin The authors of the paper revisited the compound Poisson model with i.i.d. gamma claim sizes. This model allows for two different parametrizations, the Poisson-gamma parametrization and Tweedie's compound Poisson parametrization. The results derived illustrate when these two parametrizations are identical. The main theoretical results of the paper give conditions under which the different generalized linear model parametrizations lead to identical predictive models. These results provide a remarkable property that allows to lower calibration in Tweedie's double generalized linear models. In the applied part, authors of the paper analyze why the insurance industry gives preference to the Poisson-gamma parametrization. Based on examples, authors find that, this parametrization is easier to fit, and results turn out to be more accurate. In addition, the examples under consideration show that the Tweedie version is computationally clearly lacking behind the Poisson-gamma case. Reviewer: Jonas Šiaulys (Vilnius) Exponential bounds of ruin probabilities for non-homogeneous risk models https://www.zbmath.org/1485.91212 2022-06-24T15:10:38.853281Z "Zhou, Qianqian" https://www.zbmath.org/authors/?q=ai:zhou.qianqian "Sakhanenko, Alexander" https://www.zbmath.org/authors/?q=ai:sakhanenko.aleksandr-ivanovich "Guo, Junyi" https://www.zbmath.org/authors/?q=ai:guo.junyi Summary: Lundberg-type inequalities for ruin probabilities of non-homogeneous risk models are presented. By employing the martingale method, upper bounds of ruin probabilities are obtained for general risk models under weak assumptions. In addition, several risk models, including the newly defined united risk model and a quasi-periodic risk model with interest rate, are studied. Robust identification of investor beliefs https://www.zbmath.org/1485.91224 2022-06-24T15:10:38.853281Z "Chen, Xiaohong" https://www.zbmath.org/authors/?q=ai:chen.xiaohong.2 "Hansen, Lars Peter" https://www.zbmath.org/authors/?q=ai:hansen.lars-peter "Hansen, Peter G." https://www.zbmath.org/authors/?q=ai:hansen.peter-g Summary: This paper develops a method informed by data and models to recover information about investor beliefs. Our approach uses information embedded in forward-looking asset prices in conjunction with asset pricing models. We step back from presuming rational expectations and entertain potential belief distortions bounded by a statistical measure of discrepancy. Additionally, our method allows for the direct use of sparse survey evidence to make these bounds more informative. Within our framework, market-implied beliefs may differ from those implied by rational expectations due to behavioral/psychological biases of investors, ambiguity aversion, or omitted permanent components to valuation. Formally, we represent evidence about investor beliefs using a nonlinear expectation function deduced using model-implied moment conditions and bounds on statistical divergence. We illustrate our method with a prototypical example from macrofinance using asset market data to infer belief restrictions for macroeconomic growth rates. The closed-form option pricing formulas under the sub-fractional Poisson volatility models https://www.zbmath.org/1485.91232 2022-06-24T15:10:38.853281Z "Wang, XiaoTian" https://www.zbmath.org/authors/?q=ai:wang.xiaotian "Yang, ZiJian" https://www.zbmath.org/authors/?q=ai:yang.zijian "Cao, PiYao" https://www.zbmath.org/authors/?q=ai:cao.piyao "Wang, ShiLin" https://www.zbmath.org/authors/?q=ai:wang.shilin Summary: A new fractional process called the sub-fractional Poisson process $$N_H(t)$$ is proposed, which has continuous sample paths, long- memory, leptokurtosis and heavy tail distribution, is of convenience to price options and simulate the variance process of risk asset return. Based on the sub-fractional Poisson process $$N_H(t)$$ the new fractional variance processes have been proposed, which may capture the skewness and the long-memory as well as mean-reverting in the stock price volatilities. In particular, the characteristic function method for option pricing is given, and the analytical formulas for European option price $$C(t,S_t)$$ have been obtained under the risk-neutral probability measure. Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling https://www.zbmath.org/1485.91235 2022-06-24T15:10:38.853281Z "Sheraz, Muhammad" https://www.zbmath.org/authors/?q=ai:sheraz.muhammad "Preda, Vasile" https://www.zbmath.org/authors/?q=ai:preda.vasile-c "Dedu, Silvia" https://www.zbmath.org/authors/?q=ai:dedu.silvia-cristina Summary: A minimal entropy martingale measure problem is studied to investigate risk-neutral densities and interest rate modelling. Hunt \& Devolder focused on the method of Shannon minimal entropy martingale measure to select the best measure among all the equivalent martingale measures and, proposed a generalization of the Ho \& Lee model in the semi-Markov regime-switching framework [\textit{J. Hunt} and \textit{P. Devolder}, Semi-Markov regime switching interest rate models and minimal entropy measure'', Physica A 390, No. 21--22, 3767--3781 (2011; \url{doi:10.1016/j.physa.2011.04.036})]. We formulate and solve the optimization problem of Hunt \& Devolder for deriving risk-neutral densities using a new non-extensive entropy measure [\textit{F. Shafee}, IMA J. Appl. Math. 72, No. 6, 785--800 (2007; Zbl 1180.82007)]. We use the Lambert function and a new type of approach to obtain results without depending on stochastic calculus techniques. Novel numerical techniques based on mimetic finite difference method for pricing two dimensional options https://www.zbmath.org/1485.91247 2022-06-24T15:10:38.853281Z "Attipoe, David Sena" https://www.zbmath.org/authors/?q=ai:attipoe.david-sena "Tambue, Antoine" https://www.zbmath.org/authors/?q=ai:tambue.antoine Summary: The Black-Scholes differential operator which underlies the option pricing of European and American options is known to be degenerate close to the boundary at zero. At this singularity, important properties of the differential operator are lost and the classical finite difference scheme applied to this problem fails to give accurate approximations as it is no longer monotone. In this paper novel numerical techniques based on mimetic finite difference method are proposed for accurately pricing European and American options. More precisely, we propose the mimetic and fitted mimetic finite difference methods, which are techniques that preserve and conserve general properties of the continuum operator in the discrete case. The fitted method further handles the degeneracy of the underlying partial differential equations (PDE). Those spatial discretization methods are coupled with the Euler implicit method for time discretization. Several numerical simulations are performed to demonstrate the robustness of our methods comparing to standard fitted finite volume method for both European and American put options. Shot noise, weak convergence and diffusion approximations https://www.zbmath.org/1485.92027 2022-06-24T15:10:38.853281Z "Tamborrino, Massimiliano" https://www.zbmath.org/authors/?q=ai:tamborrino.massimiliano "Lansky, Petr" https://www.zbmath.org/authors/?q=ai:lansky.petr Summary: Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise processes and prove their weak convergence to Lévy-driven Ornstein-Uhlenbeck (OU) process, whose features depend on the underlying jump distributions. Among others, we obtain the OU-gamma and OU-inverse Gaussian processes, having gamma and inverse Gaussian processes as background Lévy processes, respectively. Then, we derive the necessary conditions guaranteeing the diffusion limit to a Gaussian OU process, show that they are not met unless allowing for negative jumps happening with probability going to zero, and quantify the error occurred when replacing the shot noise with the OU process and the non-Gaussian OU processes. The results offer a new class of models to be used instead of the commonly applied Gaussian OU processes to approximate synaptic input currents, membrane voltages or conductances modelled by shot noise in single neuron modelling. Approximate controllability of noninstantaneous impulsive Hilfer fractional integrodifferential equations with fractional Brownian motion https://www.zbmath.org/1485.93055 2022-06-24T15:10:38.853281Z "Ahmed, Hamdy M." https://www.zbmath.org/authors/?q=ai:ahmed.hamdy-m "El-Borai, Mahmoud M." https://www.zbmath.org/authors/?q=ai:el-borai.mahmoud-m "El Bab, A. S. Okb" https://www.zbmath.org/authors/?q=ai:okb-el-bab.a-s "Ramadan, M. Elsaid" https://www.zbmath.org/authors/?q=ai:ramadan.m-elsaid Summary: We introduce the investigation of approximate controllability for a new class of nonlocal and noninstantaneous impulsive Hilfer fractional neutral stochastic integrodifferential equations with fractional Brownian motion. An appropriate set of sufficient conditions is derived for the considered system to be approximately controllable. For the main results, we use fractional calculus, stochastic analysis, fractional power of operators and Sadovskii's fixed point theorem. At the end, an example is also given to show the applicability of our obtained theory. A mean-field optimal control for fully coupled forward-backward stochastic control systems with Lévy processes https://www.zbmath.org/1485.93631 2022-06-24T15:10:38.853281Z "Huang, Zhen" https://www.zbmath.org/authors/?q=ai:huang.zhen "Wang, Ying" https://www.zbmath.org/authors/?q=ai:wang.ying.3 "Wang, Xiangrong" https://www.zbmath.org/authors/?q=ai:wang.xiangrong Summary: This paper is concerned with a class of mean-field type stochastic optimal control systems, which are governed by fully coupled mean-field forward-backward stochastic differential equations with Teugels martingales associated to Lévy processes. In these systems, the coefficients contain not only the state processes but also their marginal distribution, and the cost function is of mean-field type as well. The necessary and sufficient conditions for such optimal problems are obtained. Furthermore, the applications to the linear quadratic stochastic optimization control problem are investigated. Risk-sensitive optimal stopping with unbounded terminal cost function https://www.zbmath.org/1485.93633 2022-06-24T15:10:38.853281Z "Jelito, Damian" https://www.zbmath.org/authors/?q=ai:jelito.damian "Stettner, Łukasz" https://www.zbmath.org/authors/?q=ai:stettner.lukasz Summary: In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller-Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have multiple solutions and we give a probabilistic interpretation for the minimal and the maximal one. Also, we show how to approximate them using finite time horizon problems. The analysis, covering both discrete and continuous time case, is supported with illustrative examples. A time-changed stochastic control problem and its maximum principle maximum principle https://www.zbmath.org/1485.93637 2022-06-24T15:10:38.853281Z "Nane, Erkan" https://www.zbmath.org/authors/?q=ai:nane.erkan "Ni, Yinan" https://www.zbmath.org/authors/?q=ai:ni.yinan Summary: This paper studies a time-changed stochastic control problem, where the underlying stochastic process is a Lévy noise time-changed by an inverse subordinator. We establish a maximum principle for the time-changed stochastic control problem. We also prove the existence and uniqueness of the corresponding time-changed backward stochastic differential equation involved in the stochastic control problem. Some examples are provided for illustration. Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control https://www.zbmath.org/1485.93642 2022-06-24T15:10:38.853281Z "Xu, Zhenda" https://www.zbmath.org/authors/?q=ai:xu.zhenda Summary: This paper concerns a kind of stochastic optimal control problem with recursive utility described by a reflected backward stochastic differential equation (RBSDE, for short) involving diffusion type control which covers regular control problem, singular control problem and impulse control problem. To begin with, the existence and uniqueness of solution for RBSDEs involving diffusion type control is derived. Then, for the related recursive optimal control problem with obstacle constraint, a sufficient condition to obtain the optimal regular control and diffusion type control is provided. Hence, based on the connection between RBSDE and optimal stopping problem, a class of recursive optimal mixed control problem involving diffusion type control is considered to illustrate our theoretical result, and here the explicit optimal control as well as the stopping time are obtained.