Fixed point theorems and explicit estimates for convergence rates of continuous time Markov chains

Fixexd point theory and applications

Zhenhai Yan¹  Ikudol Miyamoto²  Guojun Yan³ 

[1] School of Mathematics and Statistics, Central South University, Changsha, China;School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China;School of Statistics, Henan University of Economics and Law, Zhengzhou, China

关键词: exponential ergodicity;    Markov chain;    fixed point theorem;    Poisson point process;   

DOI  :  10.1186/s13663-015-0443-x

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper we give Banach fixed point theorems and explicit estimates on the rates of convergence of the transition function to the stationary distribution for a class of exponential ergodic Markov chains. Our results are different from earlier estimates using coupling theory, and from estimates using stochastically monotone one. Our estimates show a noticeable improvement on existing results if Markov chains contain instantaneous states or nonconservative states. The proof uses existing results of discrete time Markov chains together with h-skeleton. At last, we apply this result, Ray-Knight compactification and Itô excursion theory to two examples: a class of singular Markov chains and Kolmogorov matrix.

【 授权许可】

CC BY