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作者：Bobkov, Sergey G.; Chistyakov, Gennadiy P.; Goetze, Friedrich
作者单位：University of Minnesota System; University of Minnesota Twin Cities; University of Bielefeld
摘要：An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.
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作者：Li, Xiang-Dong
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
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作者：Krylov, N. V.
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：We prove the dynamic programming principle for uniformly nondegenerate stochastic differential games in the framework of time-homogeneous diffusion processes considered up to the first exit time from a domain. In contrast with previous results established for constant stopping times we allow arbitrary stopping times and randomized ones as well. There is no assumption about solvability of the the Isaacs equation in any sense (classical or viscosity). The zeroth-order coefficient and the free te...
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作者：Kifer, Yuri; Varadhan, S. R. S.
作者单位：Hebrew University of Jerusalem; New York University
摘要：We obtain large deviations theorems for both discrete time expressions of the form and similar expressions of the form in continuous time. Here or is a Markov process satisfying Doeblin's condition, is a bounded continuous function and for while for they are positive functions taking on integer values on integers with some growth conditions which are satisfied, for instance, when 's are polynomials of increasing degrees. Applications to some types of dynamical systems such as mixing subshifts ...
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作者：Gaudilliere, A.; Landim, C.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Universite de Rouen Normandie; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an application we prove a some recurrence theorems. In particular, we show the recurrence of two-dimensional cycle random walks under a second moment condition on the winding numbers.
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作者：Thomine, Damien
作者单位：Universite de Rennes
摘要：We prove a generalized central limit theorem for dynamical systems with an infinite ergodic measure which induce a Gibbs-Markov map on some subset, provided the return time to this subset has regularly varying tails. We adapt a method designed by Csaki and Foldes for observables of random walks to show that the partial sums of some functions of the system-the return time and the observable-are asymptotically independent. Some applications to random walks and Pomeau-Manneville maps are discussed.
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作者：Kallenberg, Olav
作者单位：Auburn University System; Auburn University
摘要：Let be a locally compact topological group, acting measurably on some Borel spaces and , and consider some jointly stationary random measures on and on such that a.s. Then there exists a stationary random kernel from to such that a.s. This follows from the existence of an invariant kernel from to such that whenever . Also included are some related results on stationary integration, absolute continuity, and ergodic decomposition.
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作者：Offret, Yoann
作者单位：University of Neuchatel
摘要：We consider a family of one-dimensional diffusions, in dynamical Wiener mediums, which are random perturbations of the Ornstein-Uhlenbeck diffusion process. We prove quenched and annealed convergences in distribution and under weigh-ted total variation norms. We find two kind of stationary probability measures, which are either the standard normal distribution or a quasi-invariant measure, depending on the environment, and which is naturally connected to a random dynamical system. We apply the...
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作者：Berestycki, Julien; Berestycki, Nathanael; Schweinsberg, Jason
作者单位：Sorbonne Universite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; University of California System; University of California San Diego
摘要：We consider branching Brownian motion on the real line with absorption at zero, in which particles move according to independent Brownian motions with the critical drift of -root 2. Kesten (Stoch Process 7:9-47, 1978) showed that almost surely this process eventually dies out. Here we obtain upper and lower bounds on the probability that the process survives until some large time t. These bounds improve upon results of Kesten (Stoch Process 7:9-47, 1978), and partially confirm nonrigorous pred...
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作者：Goodman, Jesse; den Hollander, Frank
作者单位：Leiden University - Excl LUMC; Leiden University
摘要：The path of a Brownian motion on a -dimensional torus run for time is a random compact subset of . We study the geometric properties of the complement as for . In particular, we show that the largest regions in have a linear scale , where is the capacity of the unit ball. More specifically, we identify the sets for which contains a translate of , and we count the number of disjoint such translates. Furthermore, we derive large deviation principles for the largest inradius of as and the -cover ...
