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On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities

Author

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  • Haruna Okamura

    (Kansai University)

  • Toshihiro Uemura

    (Kansai University)

Abstract

We consider symmetric stable-type processes with degenerate/singular Lévy densities via Dirichlet form theory. We give conditions of some global path properties of the processes such as recurrence, transience or conservativeness. We also show the polarity of a point.

Suggested Citation

  • Haruna Okamura & Toshihiro Uemura, 2021. "On Symmetric Stable-Type Processes with Degenerate/Singular Lévy Densities," Journal of Theoretical Probability, Springer, vol. 34(2), pages 809-826, June.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:2:d:10.1007_s10959-020-00990-6
    DOI: 10.1007/s10959-020-00990-6
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    References listed on IDEAS

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    1. Chen, Zhen-Qing & Kumagai, Takashi, 2003. "Heat kernel estimates for stable-like processes on d-sets," Stochastic Processes and their Applications, Elsevier, vol. 108(1), pages 27-62, November.
    2. T. Uemura, 2004. "On Symmetric Stable-Like Processes: Some Path Properties and Generators," Journal of Theoretical Probability, Springer, vol. 17(3), pages 541-555, July.
    3. Aleksander Janicki & Aleksander Weron, 1994. "Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes," HSC Books, Hugo Steinhaus Center, Wroclaw University of Science and Technology, number hsbook9401, December.
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    Cited by:

    1. Yuichi Shiozawa, 2023. "Transience of symmetric nonlocal Dirichlet forms," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 2121-2149, May.

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