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Irreducible decomposition for Markov processes

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  • Kuwae, Kazuhiro

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.

Suggested Citation

  • Kuwae, Kazuhiro, 2021. "Irreducible decomposition for Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 140(C), pages 339-356.
    • Handle: RePEc:eee:spapps:v:140:y:2021:i:c:p:339-356
    DOI: 10.1016/j.spa.2021.06.012
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    Cited by:

    1. Liping Li & Hanlai Lin, 2023. "On Order Isomorphisms Intertwining Semigroups for Dirichlet Forms," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1304-1320, June.

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