IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v111y2004i1p41-55.html
   My bibliography  Save this article

Rate of convergence of some self-attracting diffusions

Author

Listed:
  • Herrmann, Samuel
  • Scheutzow, Michael

Abstract

We consider the rate of convergence of the paths of some self-attracting diffusions. We prove that these diffusions are attracted by their mean-process. Moreover, under some assumptions on the interaction function f, this attraction becomes strong enough to imply the almost sure convergence of the paths. In this case, we provide an estimate of the rate of convergence which depends on the growth of f near the origin.

Suggested Citation

  • Herrmann, Samuel & Scheutzow, Michael, 2004. "Rate of convergence of some self-attracting diffusions," Stochastic Processes and their Applications, Elsevier, vol. 111(1), pages 41-55, May.
    • Handle: RePEc:eee:spapps:v:111:y:2004:i:1:p:41-55
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(03)00174-1
    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. Shen, Leyi & Xia, Xiaoyu & Yan, Litan, 2022. "Least squares estimation for the linear self-repelling diffusion driven by α-stable motions," Statistics & Probability Letters, Elsevier, vol. 181(C).
    2. Xichao Sun & Litan Yan & Yong Ge, 2022. "The Laws of Large Numbers Associated with the Linear Self-attracting Diffusion Driven by Fractional Brownian Motion and Applications," Journal of Theoretical Probability, Springer, vol. 35(3), pages 1423-1478, September.
    3. Litan Yan & Yu Sun & Yunsheng Lu, 2008. "On the Linear Fractional Self-attracting Diffusion," Journal of Theoretical Probability, Springer, vol. 21(2), pages 502-516, 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:111:y:2004:i:1:p:41-55. 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.