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Dirichlet heat kernel for unimodal Lévy processes

Author

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  • Bogdan, Krzysztof
  • Grzywny, Tomasz
  • Ryznar, Michał

Abstract

We estimate the heat kernel of the smooth open set for the isotropic unimodal pure-jump Lévy process with infinite Lévy measure and weakly scaling Lévy–Khintchine exponent.

Suggested Citation

  • Bogdan, Krzysztof & Grzywny, Tomasz & Ryznar, Michał, 2014. "Dirichlet heat kernel for unimodal Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3612-3650.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:11:p:3612-3650
    DOI: 10.1016/j.spa.2014.06.001
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    References listed on IDEAS

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    1. Sztonyk, Pawel, 2011. "Transition density estimates for jump Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1245-1265, June.
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    Cited by:

    1. Cho, Soobin & Kim, Panki, 2020. "Estimates on the tail probabilities of subordinators and applications to general time fractional equations," Stochastic Processes and their Applications, Elsevier, vol. 130(7), pages 4392-4443.
    2. Grzywny, Tomasz & Kim, Kyung-Youn & Kim, Panki, 2020. "Estimates of Dirichlet heat kernel for symmetric Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 130(1), pages 431-470.
    3. Grzywny, Tomasz & Kwaśnicki, Mateusz, 2018. "Potential kernels, probabilities of hitting a ball, harmonic functions and the boundary Harnack inequality for unimodal Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 128(1), pages 1-38.
    4. Leżaj, Łukasz, 2024. "Non-symmetric stable processes: Dirichlet heat kernel, Martin kernel and Yaglom limit," Stochastic Processes and their Applications, Elsevier, vol. 174(C).

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