Algebraic convergence for discrete-time ergodic Markov chains  

作　　者：毛永华 

机构地区：[1]Department of Mathematics, Beijing Normal University, Beijing 100875, China

出　　处：《Science China Mathematics》2003年第5期621-630,共10页中国科学：数学（英文版）

基　　金：This work was supported in part by the 973 Project;the Research Fund for the Doctoral Program of Higher Education(Grant No.20010027007);the National Natural Science Foundation of China(Grant No,10121101); the National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10025105).

摘　　要：This paper studies the lergodicity for discrete-time recurrent Markov chains. It proves that thel-order deviation matrix exists and is finite if and only if the chain is (l+ 2)-ergodic, and then the algebraic decay rates of then-step transition probability to the stationary distribution are obtained. The criteria forl-ergodicity are given in terms of existence of solution to an equation. The main results are illustrated by some examples.This paper studies the e-ergodicity for discrete-time recurrent Markov chains. It proves that thee-order deviation matrix exists and is finite if and only if the chain is (e + 2)-ergodic, and then the algebraicdecay rates of the n-step transition probability to the stationary distribution are obtained. The criteria fore-ergodicity are given in terms of existence of solution to an equation. The main results are illustrated by some examples.

关 键 词：MARKOV chain  ergodicity  ALGEBRAIC convergence  deviation matrix. 

分 类 号：O211.62[理学—概率论与数理统计]