强遍历Markov链的扰动估计及收敛速度  

Perturbation Bounds and Convergence Rates for Uniformly Ergodic Markov Chains

作　　者：宋延红[1] 毛永华[2] Yan Hong SONG;Yong Hua MAO(School of Statistics and Mathematics,Zhongnan University of Economics and Law,Wuhan 430073,P.R.China;School of Mathematical Sciences,Beijing Normal University,Laboratory of Mathematics and Compler Systems,Ministry of Education,Beijing 100875,P.R.China)

机构地区：[1]中南财经政法大学统计与数学学院,武汉430073 [2]北京师范大学数学科学学院数学与复杂系统教育部重点实验室,北京100875

出　　处：《数学学报（中文版）》2023年第4期599-616,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(11771047,11501576);国家重点研发计划资助项目(2020YFA0712900)。

摘　　要：本文利用首次击中时的一致阶矩研究了一般状态空间强遍历Markov链的扰动估计和收敛速度.对可逆非负定Markov链,我们首先用谱理论研究了几何遍历的收敛速度.基于此估计和首次通过公式,接着研究了强遍历的收敛速度和扰动估计.若Markov链只是可逆的,我们通过研究以P2为转移核的骨架链得到P的相应性质.最后,讨论了一般Markov链的扰动估计.We study perturbation bounds and convergence rates for uniformly ergodic Markov chains on general state spaces in terms of uniform moments of the first hitting times on some set.For reversible and non-negative definite Markov chains,we first investigate the geometrically ergodic convergence rates by the spectral theory.Based on the estimates,together with a first passage formula,we then get the convergence rates and perturbation bounds of uniform ergodicity.If the Markov chain is only reversible,we transfer to study the skeleton chain with transition kernel P2.Finally,we investigate perturbation bounds for general Markov chains.

关 键 词：MARKOV链 扰动估计 强遍历 首次击中时 首次回返时 

分 类 号：O211.62[理学—概率论与数理统计]