Poisson limit law for Markov chains-Reference-Cited by-同舟云学术

Poisson limit law for Markov chains

Published:1991-09 Issue:3 Volume:11 Page:501-513
ISSN:0143-3857
Container-title:Ergodic Theory and Dynamical Systems
language:en
Short-container-title:Ergod. Th. Dynam. Sys.

Author:

Pitskel B.

Abstract

AbstractFor a mixing stationary Markov chain we prove a Poisson limit law for the recurrence to small cylindrical sets. Since hyperbolic torus automorphisms are Markov chains, the result carries over to these transformations.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,General Mathematics

Reference5 articles.

1. ENTROPY, A COMPLETE METRIC INVARIANT FOR AUTOMORPHISMS OF THE TORUS

2. Ergodic Theory

3. On the strong law of large numbers for a class of stochastic processes

4. Poisson limit law for a scheme of sums of independent random variables;Sevast'yanov;Theory of Probability and its Applications,1972

Cited by 85 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Number of visits in arbitrary sets for ϕ-mixing dynamics;Annales de l'Institut Henri Poincaré, Probabilités et Statistiques;2024-05-01

2. Poisson Limit Distribution for Diffeomorphisms with Weak Hyperbolic Product Structure;Real Analysis Exchange;2023-10-01

3. Singular value distribution of dense random matrices with block Markovian dependence;Stochastic Processes and their Applications;2023-04

4. Quenched Poisson processes for random subshifts of finite type;Nonlinearity;2022-06-02

5. Poisson Approximations and Convergence Rates for Hyperbolic Dynamical Systems;Communications in Mathematical Physics;2022-01-19