Convergence rates for reversible Markov chains without the assumption of nonnegative definite matrices  

作　　者：MAO Yong-Hua School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Complex Systems,Ministry of Education,Beijing 100875,China 

出　　处：《Science China Mathematics》2010年第8期1979-1988,共10页中国科学：数学（英文版）

基　　金：supported by Program for New Century Excellent Talents in University,National Basic Research Program of China (973 Project) (Grant No.2006CB805901);National Natural Science Foundation of China (Grant No.10721091)

摘　　要：Explicit convergence rates in geometric and strong ergodicity for denumerable discrete time Markov chains with general reversible transition matrices are obtained in terms of the geometric moments or uniform moments of the hitting times to a fixed point.Another way by Lyapunov's drift conditions is also used to derive these convergence rates.As a typical example,the discrete time birth-death process(random walk) is studied and the explicit criteria for geometric ergodicity are presented.Explicit convergence rates in geometric and strong ergodicity for denumerable discrete time Markov chains with general reversible transition matrices are obtained in terms of the geometric moments or uniform moments of the hitting times to a fixed point.Another way by Lyapunov’s drift conditions is also used to derive these convergence rates.As a typical example,the discrete time birth-death process(random walk) is studied and the explicit criteria for geometric ergodicity are presented.

关 键 词：MARKOV chain spectral theory convergence rate geometric ERGODICITY strong ERGODICITY Lyapunov’s condition 

分 类 号：O211.62[理学—概率论与数理统计]