Coupling Approach And The Ergodicity Of Markov Chains

In this paper, we apply coupling methods to study ergodicity for Markov pro-cesses, and sufficient conditions are presented in terms of the expectations of coupling times, and prove|a*u(n)-b*u(n)|â†'0and its summable is limite.Since the coupling methods are introduced by Doeblin,it has been aroused the concern of scholars home and abroad because of its catholic application on Markov processes.However coupling process and the ergodicity of Markov process combined with very closely, so this article will introduce from the following aspects;The first.we introduced the basic knowledge of renewal process and coupling,and the coupling of renewal processes and main results are presented;The second.Generally,Renewal processes are not markov processes,so we intro-duce the concept of Forward recurrencetime chains,and nature and those coupling;The third.On the basic of the second part,in order to prove the Ergodicity of Markov processes,we define a stationary distribution,and structure a sequence which is independent and identically distributed;Finally,We expounds∑n|a*u(n)-b*u(n)|<∞...