Irreducible decomposition for Markov processes

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:140

Article

Kuwae, Kazuhiro¹ 

[1] Fukuoka Univ, Fac Sci, Dept Appl Math, Fukuoka 8140180, Japan

关键词: Semi-Dirichlet forms;    Ergodicity;    Irreducibility;    Absolute continuity condition;    Quasi-Lindelof property;    Chacon-Ornstein ergodic theorem;   

DOI  :  10.1016/j.spa.2021.06.012

来源: Elsevier

【 摘 要 】

We prove an irreducible decomposition for Markov processes associated with quasi-regular symmetric Dirichlet forms or local semi-Dirichlet forms under the absolute continuity condition of transition probability with respect to the underlying measure. We do not assume the conservativeness nor the existence of invariant measures for the processes. As applications, we establish a concrete expression for Chacon-Ornstein type ratio ergodic theorem for such Markov processes and show a compactness of semi-groups under the Green-tightness of measures in the framework of symmetric resolvent strong Feller processes without irreducibility. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free