IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v126y2016i3p703-734.html
   My bibliography  Save this article

Solutions of martingale problems for Lévy-type operators with discontinuous coefficients and related SDEs

Author

Listed:
  • Imkeller, Peter
  • Willrich, Niklas

Abstract

We show the existence of Lévy-type stochastic processes in one space dimension with characteristic triplets that are either discontinuous at thresholds, or are stable-like with stability index functions for which the closures of the discontinuity sets are countable. For this purpose, we formulate the problem in terms of a Skorokhod-space martingale problem associated with non-local operators with discontinuous coefficients. These operators are approximated along a sequence of smooth non-local operators giving rise to Feller processes with uniformly controlled symbols. They converge uniformly outside of increasingly smaller neighborhoods of a Lebesgue null set on which the singularities of the limit operator are located.

Suggested Citation

  • Imkeller, Peter & Willrich, Niklas, 2016. "Solutions of martingale problems for Lévy-type operators with discontinuous coefficients and related SDEs," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 703-734.
    • Handle: RePEc:eee:spapps:v:126:y:2016:i:3:p:703-734
    DOI: 10.1016/j.spa.2015.09.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915002458
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.09.017?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. Bass, Richard F. & Tang, Huili, 2009. "The martingale problem for a class of stable-like processes," Stochastic Processes and their Applications, Elsevier, vol. 119(4), pages 1144-1167, April.
    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. Chen, Xin & Chen, Zhen-Qing & Wang, Jian, 2020. "Heat kernel for non-local operators with variable order," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3574-3647.
    2. Xi, Fubao & Zhu, Chao, 2018. "On the martingale problem and Feller and strong Feller properties for weakly coupled Lévy type operators," Stochastic Processes and their Applications, Elsevier, vol. 128(12), pages 4277-4308.
    3. Peng Jin, 2021. "Uniqueness in Law for Stable-Like Processes of Variable Order," Journal of Theoretical Probability, Springer, vol. 34(2), pages 522-552, 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:126:y:2016:i:3:p:703-734. 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.