IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v22y2009i4d10.1007_s10959-008-0180-8.html
   My bibliography  Save this article

Stationarity and Self-Similarity Characterization of the Set-Indexed Fractional Brownian Motion

Author

Listed:
  • Erick Herbin

    (Ecole Centrale Paris)

  • Ely Merzbach

    (Bar Ilan University)

Abstract

The set-indexed fractional Brownian motion (sifBm) has been defined by Herbin–Merzbach (J. Theor. Probab. 19(2):337–364, 2006) for indices that are subsets of a metric measure space. In this paper, the sifBm is proved to satisfy a strengthened definition of increment stationarity. This new definition for stationarity property allows us to get a complete characterization of this process by its fractal properties: The sifBm is the only set-indexed Gaussian process which is self-similar and has stationary increments. Using the fact that the sifBm is the only set-indexed process whose projection on any increasing path is a one-dimensional fractional Brownian motion, the limitation of its definition for a self-similarity parameter 0

Suggested Citation

  • Erick Herbin & Ely Merzbach, 2009. "Stationarity and Self-Similarity Characterization of the Set-Indexed Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 22(4), pages 1010-1029, December.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:4:d:10.1007_s10959-008-0180-8
    DOI: 10.1007/s10959-008-0180-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-008-0180-8
    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/s10959-008-0180-8?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Paul Balança, 2015. "An Increment-Type Set-Indexed Markov Property," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1271-1310, December.

    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:22:y:2009:i:4:d:10.1007_s10959-008-0180-8. 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: 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.