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On the Conservativeness of Some Markov Processes

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Abstract

We give a unified method to obtain the conservativeness of a class of Markov processes associated with lower bounded semi-Dirichlet forms on L 2(X;m), including symmetric diffusion processes, some non-symmetric diffusion processes and jump type Markov processes on X, where X is a locally compact separable metric space and m is a positive Radon measure on X with full topological support. Using the method, we give an example in each section, providing the conservativeness of the processes, that are given by the “increasingness of the volume of some sets(balls)” and “that of the coefficients on the sets” of the Markov processes.

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Authors and Affiliations

  1. Kumamoto University, Kurokami, Tyuo-ku, Kumamoto, Japan

    Yoichi Oshima

  2. Department of Mathematics, Kansai University, Yamate, Suita, Osaka, Japan

    Toshihiro Uemura

Authors
  1. Yoichi Oshima
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  2. Toshihiro Uemura
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Corresponding author

Correspondence to Toshihiro Uemura.

Additional information

This work was partially supported by JSPS(TU).

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Oshima, Y., Uemura, T. On the Conservativeness of Some Markov Processes. Potential Anal 46, 609–645 (2017). https://doi.org/10.1007/s11118-016-9596-4

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  • DOI: https://doi.org/10.1007/s11118-016-9596-4

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