Relation Between the Eventual Continuity and the E-property for Markov-Feller Semigroups  

作　　者：Yong Liu Zi-yu Liu 

机构地区：[1]LMAM,School of Mathematical Science,Peking University,Beijing,100871,China

出　　处：《Acta Mathematicae Applicatae Sinica》2024年第1期1-16,共16页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China (No.11731009, No.12231002);Center for Statistical Science,Peking University。

摘　　要：We investigate some relations between two kinds of semigroup regularities, namely the e-property and the eventual continuity, both of which contribute to the ergodicity for Markov processes on Polish spaces.More precisely, we prove that for Markov-Feller semigroup in discrete time and stochastically continuous MarkovFeller semigroup in continuous time, if there exists an ergodic measure whose support has a nonempty interior,then the e-property is satisfied on the interior of the support. In particular, it implies that, restricted on the support of each ergodic measure, the e-property and the eventual continuity are equivalent for the discrete-time and the stochastically continuous continuous-time Markov-Feller semigroups.

关 键 词：Markov-Feller semigroup ERGODICITY e-property eventual continuity 

分 类 号：O211.62[理学—概率论与数理统计] O152.7[理学—数学]