Chernoff-type bound for finite Markov chains
成果类型：
Article
署名作者：
Lezaud, P
署名单位：
Universite de Toulouse; Universite Toulouse III - Paul Sabatier
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1998
页码：
849-867
关键词：
摘要：
This paper develops bounds on the distribution function of the empirical mean for irreducible finite-state Markov chains. One approach, explored by Gillman, reduces this problem to bounding the largest eigenvalue of a perturbation of the transition matrix for the Markov chain. By using estimates on eigenvalues given in Kato's book Perturbation Theory for Linear Operators, we simplify the proof of Gillman and extend it to nonreversible finite-state Markov chains and continuous time. We also set out another method, directly applicable to some general ergodic Markov kernels having a spectral gap.