文献类型：期刊文献

英文题名：Fixed point theorems and explicit estimates for convergence rates of continuous time Markov chains

作者：Yan, Zhenhai[1,2];Yan, Guojun[3];Miyamoto, Ikudol[4]

第一作者：Yan, Zhenhai

通讯作者：Miyamoto, I[1]

机构：[1]Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China;[2]Henan Univ Econ & Law, Sch Stat, Zhengzhou 450046, Henan, Peoples R China;[3]Zhengzhou Univ, Sch Math & Stat, Zhengzhou 450001, Henan, Peoples R China;[4]Nagoya Univ, Gra Sch Math, Chikusa Ku, Nagoya, Aichi 4648601, Japan

第一机构：Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

通讯机构：[1]corresponding author), Nagoya Univ, Gra Sch Math, Chikusa Ku, Furo Cho, Nagoya, Aichi 4648601, Japan.

年份：2015

卷号：2015

期号：1

外文期刊名：FIXED POINT THEORY AND APPLICATIONS

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000364144200001)】；

语种：英文

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

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 Ito excursion theory to two examples: a class of singular Markov chains and Kolmogorov matrix.