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作者：Ceillier, Gael; Leuridan, Christophe
作者单位：Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：A. Vershik discovered that filtrations indexed by the non-positive integers may have a paradoxical asymptotic behaviour near the time , called non-standardness. For example, two dyadic filtrations with trivial tail -field are not necessarily isomorphic. Yet, from any essentially separable filtration indexed by the non-positive integers, one can extract a subsequence which is a standard filtration. In this paper, we focus on the non-standard filtrations which become standard if (and only if) in...
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作者：Barral, Julien; Jin, Xiong
作者单位：Universite Paris 13; University of Manchester
摘要：In this paper we extend some classical results valid for canonical multiplicative cascades to exact scaling log-infinitely divisible cascades. We present an alternative construction of exact scaling infinitely divisible cascades based on a family of cones whose geometry naturally induces the exact scaling property. We complete previous results on non-degeneracy and moments of positive orders obtained by Barral and Mandelbrot, and Bacry and Muzy: we provide a necessary and sufficient condition ...
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作者：Aidekon, Elie
作者单位：Sorbonne Universite
摘要：We give an expression of the speed of the biased random walk on a Galton-Watson tree. In the particular case of the simple random walk, we recover the result of Lyons et al. (Erg Theory Dyn Syst 15:593-619, 1995). The proof uses a description of the invariant distribution of the environment seen from the particle.
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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：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：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：Kifer, Yuri; Rapaport, Ariel
作者单位：Hebrew University of Jerusalem
摘要：It was shown in Kifer (Israel J Math, 2013) that for any subshift of finite type considered with a Gibbs invariant measure the numbers of multiple recurrencies to shrinking cylindrical neighborhoods of almost all points are asymptotically Poisson distributed. Here we not only extend this result to all psi-mixing shifts with countable alphabet but actually show that for all points the distributions of these numbers are asymptotically close either to Poisson or to compound Poisson distributions....
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作者：Bhamidi, Shankar; Budhiraja, Amarjit; Wang, Xuan
作者单位：University of North Carolina; University of North Carolina Chapel Hill
摘要：Random graph models with limited choice have been studied extensively with the goal of understanding the mechanism of the emergence of the giant component. One of the standard models are the Achlioptas random graph processes on a fixed set of n vertices. Here at each step, one chooses two edges uniformly at random and then decides which one to add to the existing configuration according to some criterion. An important class of such rules are the bounded-size rules where for a fixed K >= 1, all...
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作者：Yin, Jun
作者单位：University of Wisconsin System; University of Wisconsin Madison
摘要：In the first part (Bourgade et al., Local circular law for random matrices, preprint, arXiv: 1206.1449, 2012) of this article series, Bourgade, Yau and the author of this paper proved a local version of the circular law up to the finest scale N-1/2+epsilon for non-Hermitian random matrices at any point z is an element of C with parallel to z vertical bar-1 vertical bar > c for any constant c > 0 independent of the size of the matrix. In the second part (Bourgade et al., The local circular law ...
