IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v98y2002i2p317-330.html
   My bibliography  Save this article

Jumping SDEs: absolute continuity using monotonicity

Author

Listed:
  • Fournier, Nicolas

Abstract

We study the solution X={Xt}t[set membership, variant][0,T] to a Poisson-driven SDE. This equation is "irregular" in the sense that one of its coefficients contains an indicator function, which allows to generalize the usual situations: the rate of jump of X may depend on X itself. For t>0 fixed, the random variable Xt does not seem to be differentiable (with respect to the alea) in a usual sense (see e.g. Séminaire de Probabilités XVII, Lecture Notes in Mathematics, Vol. 986, Springer, Berlin, 1983, pp. 132-157), and actually not even continuous. We thus introduce a new technique, based on a sort of monotony of the map [omega]|->Xt([omega]), to prove that under quite stringent assumptions, which make possible comparison theorems, the law of Xt admits a density with respect to the Lebesgue measure on .

Suggested Citation

  • Fournier, Nicolas, 2002. "Jumping SDEs: absolute continuity using monotonicity," Stochastic Processes and their Applications, Elsevier, vol. 98(2), pages 317-330, April.
    • Handle: RePEc:eee:spapps:v:98:y:2002:i:2:p:317-330
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(01)00149-1
    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. Pagès Gilles & Rey Clément, 2019. "Recursive computation of the invariant distributions of Feller processes: Revisited examples and new applications," Monte Carlo Methods and Applications, De Gruyter, vol. 25(1), pages 1-36, March.
    2. Löcherbach, E., 2018. "Absolute continuity of the invariant measure in piecewise deterministic Markov Processes having degenerate jumps," Stochastic Processes and their Applications, Elsevier, vol. 128(6), pages 1797-1829.
    3. Fournier, Nicolas & Giet, Jean-Sébastien, 2006. "Existence of densities for jumping stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 116(4), pages 643-661, April.
    4. Du, Qiang & Toniazzi, Lorenzo & Zhou, Zhi, 2020. "Stochastic representation of solution to nonlocal-in-time diffusion," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2058-2085.

    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:98:y:2002:i:2:p:317-330. 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.