Irreducible decomposition for Markov processes

Kazuhiro Kuwae

Stochastic Processes and their Applications, 2021, vol. 140, issue C, 339-356

Abstract: 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.

Keywords: Semi-Dirichlet forms; Ergodicity; Irreducibility; Absolute continuity condition; Quasi-Lindelöf property; Chacon–Ornstein ergodic theorem (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2021.06.012

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