Correction to a proposition related to ergodicity of Markov chains  

作　　者：Ziqi TAN Xianping GUO 

机构地区：[1]School of Mathematics and Guangdong Province Key Laboratory of Computational Science,Sun Yat-sen University,Guangzhou,510275,China

出　　处：《Frontiers of Mathematics in China》2021年第3期801-813,共13页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11931018,61773411);the National Natural Science Foundation of Guangdong Province,China(Grant No.2021A1515010057);and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University,China(2020B1212060032).

摘　　要：Proposition 5.5.6(ii)in the book Markov Chains and Stochastic Stability(2nd ed,Cambridge Univ.Press,2009)has been used in the proof of a theorem about ergodicity of Markov chains.Unfortunately,an example in this paper shows that this proposition is not always true.Thus,a correction of this proposition is provided.

关 键 词：Markov chain split chain petite set minorization condition 

分 类 号：O211.62[理学—概率论与数理统计]