IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i6p907-925.html
   My bibliography  Save this article

Bismut-Elworthy's formula and random walk representation for SDEs with reflection

Author

Listed:
  • Deuschel, Jean-Dominique
  • Zambotti, Lorenzo

Abstract

We study the existence of first derivatives with respect to the initial condition of the solution of a finite system of SDEs with reflection. We prove that such derivatives evolve according to a linear differential equation when the process is away from the boundary and that they are projected to the tangent space when the process hits the boundary. This evolution, rather complicated due to the structure of the set at times when the process is at the boundary, admits a simple representation in terms of an auxiliary random walk. A probabilistic representation formula of Bismut-Elworthy's type is given for the gradient of the transition semigroup of the reflected process.

Suggested Citation

  • Deuschel, Jean-Dominique & Zambotti, Lorenzo, 2005. "Bismut-Elworthy's formula and random walk representation for SDEs with reflection," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 907-925, June.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:6:p:907-925
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(05)00012-8
    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. Deuschel, Jean-Dominique & Nishikawa, Takao, 2007. "The dynamic of entropic repulsion," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 575-595, May.
    2. Sandro Franceschi & Kilian Raschel, 2022. "A dual skew symmetry for transient reflected Brownian motion in an orthant," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 123-141, October.
    3. Avi Mandelbaum & Kavita Ramanan, 2010. "Directional Derivatives of Oblique Reflection Maps," Mathematics of Operations Research, INFORMS, vol. 35(3), pages 527-558, August.

    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:115:y:2005:i:6:p:907-925. 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.