IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i1p431-470.html
   My bibliography  Save this article

Estimates of Dirichlet heat kernel for symmetric Markov processes

Author

Listed:
  • Grzywny, Tomasz
  • Kim, Kyung-Youn
  • Kim, Panki

Abstract

We consider a large class of symmetric pure jump Markov processes dominated by isotropic unimodal Lévy processes with weak scaling conditions. First, we establish sharp two-sided heat kernel estimates for these processes in C1,1 open sets. As corollaries of our main results, we obtain sharp two-sided Green function estimates and a scale invariant boundary Harnack inequality with explicit decay rates in C1,1 open sets.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:431-470
    DOI: 10.1016/j.spa.2019.03.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414919301760
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2019.03.017?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Kim, Panki & Song, Renming & Vondraček, Zoran, 2014. "Global uniform boundary Harnack principle with explicit decay rate and its application," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 235-267.
    3. Kim, Kyung-Youn & Kim, Panki, 2014. "Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in C1,η open sets," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3055-3083.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Kim, Panki & Song, Renming & Vondraček, Zoran, 2016. "Minimal thinness with respect to subordinate killed Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1226-1263.
    4. Vondraček, Zoran & Wagner, Vanja, 2018. "On purely discontinuous additive functionals of subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 128(2), pages 707-725.
    5. Kim, Kyung-Youn & Kim, Panki, 2014. "Two-sided estimates for the transition densities of symmetric Markov processes dominated by stable-like processes in C1,η open sets," Stochastic Processes and their Applications, Elsevier, vol. 124(9), pages 3055-3083.
    6. Xie, Longjie, 2017. "Singular SDEs with critical non-local and non-symmetric Lévy type generator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3792-3824.
    7. Mimica, Ante & Vondraček, Zoran, 2014. "Unavoidable collections of balls for isotropic Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 124(3), pages 1303-1334.
    8. Ante Mimica & Stjepan Šebek, 2019. "Harnack Inequality for Subordinate Random Walks," Journal of Theoretical Probability, Springer, vol. 32(2), pages 737-764, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:130:y:2020:i:1:p:431-470. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.