IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Hurst exponents, Markov processes, and fractional Brownian motion

  • McCauley, Joseph L.
  • Gunaratne, Gemunu H.
  • Bassler, Kevin E.
Registered author(s):

    There is much confusion in the literature over Hurst exponents. Recently, we took a step in the direction of eliminating some of the confusion. One purpose of this paper is to illustrate the difference between fBm on the one hand and Gaussian Markov processes where H≠1/2 on the other. The difference lies in the increments, which are stationary and correlated in one case and nonstationary and uncorrelated in the other. The two- and one-point densities of fBm are constructed explicitly. The two-point density doesn’t scale. The one-point density for a semi-infinite time interval is identical to that for a scaling Gaussian Markov process with H≠1/2 over a finite time interval. We conclude that both Hurst exponents and one point densities are inadequate for deducing the underlying dynamics from empirical data. We apply these conclusions in the end to make a focused statement about ‘nonlinear diffusion’.

    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: http://mpra.ub.uni-muenchen.de/2154/1/MPRA_paper_2154.pdf
    File Function: original version
    Download Restriction: no

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 2154.

    as
    in new window

    Length:
    Date of creation: 30 Sep 2006
    Date of revision:
    Handle: RePEc:pra:mprapa:2154
    Contact details of provider: Postal: Schackstr. 4, D-80539 Munich, Germany
    Phone: +49-(0)89-2180-2219
    Fax: +49-(0)89-2180-3900
    Web page: http://mpra.ub.uni-muenchen.de

    More information through EDIRC

    No references listed on IDEAS
    You can help add them by filling out this form.

    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:pra:mprapa:2154. 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: (Ekkehart Schlicht)

    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.