IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v119y2009i5p1601-1631.html
   My bibliography  Save this article

Boundary Harnack principle for subordinate Brownian motions

Author

Listed:
  • Kim, Panki
  • Song, Renming
  • Vondracek, Zoran

Abstract

We establish a boundary Harnack principle for a large class of subordinate Brownian motions, including mixtures of symmetric stable processes, in [kappa]-fat open sets (disconnected analogue of John domains). As an application of the boundary Harnack principle, we identify the Martin boundary and the minimal Martin boundary of bounded [kappa]-fat open sets with respect to these processes with their Euclidean boundaries.

Suggested Citation

  • Kim, Panki & Song, Renming & Vondracek, Zoran, 2009. "Boundary Harnack principle for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 119(5), pages 1601-1631, May.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:5:p:1601-1631
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(08)00127-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Chen, Zhen-Qing & Wang, Jie-Ming, 2022. "Boundary Harnack principle for diffusion with jumps," Stochastic Processes and their Applications, Elsevier, vol. 151(C), pages 342-395.
    2. Fotopoulos, Stergios & Jandhyala, Venkata & Wang, Jun, 2015. "On the joint distribution of the supremum functional and its last occurrence for subordinated linear Brownian motion," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 149-156.
    3. Kim, Panki & Song, Renming & Vondraček, Zoran, 2013. "Potential theory of subordinate Brownian motions with Gaussian components," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 764-795.
    4. 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.
    5. Farouk Mselmi, 2022. "Generalized linear model for subordinated Lévy processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 772-801, June.
    6. Kwaśnicki, Mateusz & Małecki, Jacek & Ryznar, Michał, 2013. "First passage times for subordinate Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1820-1850.
    7. Chen, Zhen-Qing & Kim, Panki & Song, Renming, 2011. "Green function estimates for relativistic stable processes in half-space-like open sets," Stochastic Processes and their Applications, Elsevier, vol. 121(5), pages 1148-1172, May.
    8. 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.
    9. Kim, Panki & Lee, Yunju, 2013. "Oscillation of harmonic functions for subordinate Brownian motion and its applications," Stochastic Processes and their Applications, Elsevier, vol. 123(2), pages 422-445.

    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:119:y:2009:i:5:p:1601-1631. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.