IDENTIFICATION OF THE RATE FUNCTION FOR LARGE DEVIATIONS OF AN IRREDUCIBLE MARKOV CHAIN

被引：2

作者：

Liu, Wei ^{[1
]}

Wu, Liming ^{[2
,3
]}

机构：

[1] Wuhan Univ, Dept Math, Wuhan 430072, Peoples R China

[2] Univ Clermont Ferrand, CNRS, Lab Math Appl, UMR 6620, F-63177 Clermont Ferrand, France

[3] Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2009年 / 14卷

关键词：

Large deviations; irreducible Markov processes; Feynman-Kac semigroups; ASYMPTOTIC EVALUATION; PROCESS EXPECTATIONS; LARGE TIME; LOWER BOUNDS; ADDITIVE-FUNCTIONALS; LIMIT-THEOREMS;

D O I：

10.1214/ECP.v14-1512

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

For an irreducible Markov chain (X(n)) n >= 0 we identify the rate function governing the large deviation estimation of empirical mean 1/n Sigma(n-1)(k=0) f(X(k)) by means of the Donsker-Varadhan's entropy. That allows us to obtain the lower bound of large deviations for the empirical measure 1/n Sigma(n-1)(k=0) delta(Xk) in full generality.

引用

页码：540 / 551

页数：12

共 26 条

[1]

[Anonymous], 1984, CAMBRIDGE TRACTS MAT

[2] SOME FAMILIAR EXAMPLES FOR WHICH THE LARGE DEVIATION PRINCIPLE DOES NOT HOLD [J].