IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v181y2025ics0304414924002412.html
   My bibliography  Save this article

Numerical approximation of SDEs with fractional noise and distributional drift

Author

Listed:
  • Goudenège, Ludovic
  • Haress, El Mehdi
  • Richard, Alexandre

Abstract

We study the numerical approximation of SDEs with singular drifts (including distributions) driven by a fractional Brownian motion. Under the Catellier–Gubinelli condition that imposes the regularity of the drift to be strictly greater than 1−1/(2H), we obtain an explicit rate of convergence of a tamed Euler scheme towards the SDE, extending results for bounded drifts. Beyond this regime, when the regularity of the drift is 1−1/(2H), we derive a non-explicit rate. As a byproduct, strong well-posedness for these equations is recovered. Proofs use new regularising properties of discrete-time fBm and a new critical Grönwall-type lemma. We present examples and simulations.

Suggested Citation

  • Goudenège, Ludovic & Haress, El Mehdi & Richard, Alexandre, 2025. "Numerical approximation of SDEs with fractional noise and distributional drift," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002412
    DOI: 10.1016/j.spa.2024.104533
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414924002412
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2024.104533?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.

    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:181:y:2025:i:c:s0304414924002412. 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.