Multiplicative ergodicity and large deviations for an irreducible Markov chain

被引：65

作者：

Balaji, S ^{[1
]}

Meyn, SP

机构：

[1] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

[2] Univ Illinois, Coordinated Sci Lab, Urbana, IL 61801 USA

[3] Univ Illinois, Dept Elect & Comp Engn, Urbana, IL 61801 USA

[4] Indian Inst Sci, Bangalore 560012, Karnataka, India

[5] Technion Israel Inst Technol, IL-32000 Haifa, Israel

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2000年 / 90卷 / 01期

基金：

美国国家科学基金会;

关键词：

Markov chain; ergodic theory; harmonic functions; large deviations;

D O I：

10.1016/S0304-4149(00)00032-6

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：

The paper examines multiplicative ergodic theorems and the related multiplicative Poisson equation for an irreducible Markov chain on a countable state space. The partial products are considered for a real-valued function on the state space. If the function of interest satisfies a monotone condition, or is dominated by such a function, then. (i) The mean normalized products converge geometrically quickly to a finite limiting value. (ii) The multiplicative Poisson equation admits a solution. (iii) Large deviation bounds are obtainable for the empirical measures. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：123 / 144

页数：22

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