IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this article

Approximation of stationary solutions of Gaussian driven stochastic differential equations

Listed author(s):
  • Cohen, Serge
  • Panloup, Fabien
Registered author(s):

    We study sequences of empirical measures of Euler schemes associated to some non-Markovian SDEs: SDEs driven by Gaussian processes with stationary increments. We obtain the functional convergence of this sequence to a stationary solution to the SDE. Then, we end the paper by some specific properties of this stationary solution. We show that, in contrast to Markovian SDEs, its initial random value and the driving Gaussian process are always dependent. However, under an integral representation assumption, we also obtain that the past of the solution is independent of the future of the underlying innovation process of the Gaussian driving process.

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

    File URL:
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 12 ()
    Pages: 2776-2801

    in new window

    Handle: RePEc:eee:spapps:v:121:y:2011:i:12:p:2776-2801
    DOI: 10.1016/
    Contact details of provider: Web page:

    Order Information: Postal: http://

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

    in new window

    1. Lemaire, Vincent, 2007. "An adaptive scheme for the approximation of dissipative systems," Stochastic Processes and their Applications, Elsevier, vol. 117(10), pages 1491-1518, October.
    2. Gilles Pag\`es & Fabien Panloup, 2007. "Approximation of the distribution of a stationary Markov process with application to option pricing," Papers 0704.0335,, revised Sep 2009.
    3. Crauel, Hans, 1993. "Non-Markovian invariant measures are hyperbolic," Stochastic Processes and their Applications, Elsevier, vol. 45(1), pages 13-28, March.
    Full references (including those not matched with items on IDEAS)

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:121:y:2011:i:12:p:2776-2801. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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

    This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.