Probability Theory and Related Fields

最新文章

• Filtrations at the threshold of standardness AI翻译
  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...
• On exact scaling log-infinitely divisible cascades AI翻译
  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 ...
• Speed of the biased random walk on a Galton-Watson tree AI翻译
  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.
• Fisher information and the central limit theorem AI翻译
  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.
• Martingale transforms and Lp-norm estimates of Riesz transforms on complete Riemannian manifolds (vol 141, pg 247, 2008) AI翻译
  作者：Li, Xiang-Dong
  作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier
• On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations AI翻译
  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...
• Nonconventional large deviations theorems AI翻译
  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 ...
• A Dirichlet principle for non reversible Markov chains and some recurrence theorems AI翻译
  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.
• A generalized central limit theorem in infinite ergodic theory AI翻译
  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.
• Stationary and invariant densities and disintegration kernels AI翻译
  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.