IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v25y2012i4d10.1007_s10959-011-0351-x.html
   My bibliography  Save this article

Self-intersection Local Time of Planar Brownian Motion Based on a Strong Approximation by Random Walks

Author

Listed:
  • Tamás Szabados

    (Budapest University of Technology and Economics)

Abstract

The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian motion by simple, symmetric random walks. As a result, Brownian self-intersection local time is obtained as an almost sure limit of local averages of simple random walk self-intersection local times. An important tool is a discrete version of the Tanaka–Rosen–Yor formula; the continuous version of the formula is obtained as an almost sure limit of the discrete version. The author hopes that this approach to self-intersection local time is more transparent and elementary than other existing ones.

Suggested Citation

  • Tamás Szabados, 2012. "Self-intersection Local Time of Planar Brownian Motion Based on a Strong Approximation by Random Walks," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1081-1118, December.
    • Handle: RePEc:spr:jotpro:v:25:y:2012:i:4:d:10.1007_s10959-011-0351-x
    DOI: 10.1007/s10959-011-0351-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-011-0351-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-011-0351-x?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.

    References listed on IDEAS

    as
    1. Tamás Szabados & Balázs Székely, 2009. "Stochastic Integration Based on Simple, Symmetric Random Walks," Journal of Theoretical Probability, Springer, vol. 22(1), pages 203-219, March.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      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:spr:jotpro:v:25:y:2012:i:4:d:10.1007_s10959-011-0351-x. 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.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc 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 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

      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.