Advanced Search
MyIDEAS: Login to save this article or follow this journal

Sub-fractional Brownian motion and its relation to occupation times

Contents:

Author Info

  • Bojdecki, Tomasz
  • Gorostiza, Luis G.
  • Talarczyk, Anna
Registered author(s):

    Abstract

    We study a long-range dependence Gaussian process which we call "sub-fractional Brownian motion" (sub-fBm), because it is intermediate between Brownian motion (Bm) and fractional Brownian motion (fBm) in the sense that it has properties analogous to those of fBm, but the increments on non-overlapping intervals are more weakly correlated and their covariance decays polynomially at a higher rate. Sub-fBm has a parameter h[set membership, variant](0,2), we show how it arises from occupation time fluctuations of branching particle systems for h[greater-or-equal, slanted]1 and we exhibit the long memory effect of the initial condition.

    Download Info

    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://www.sciencedirect.com/science/article/B6V1D-4CX6RJK-2/2/2d042cf20dbe3956cd32dbbcfa9bbff2
    Download Restriction: Full text for ScienceDirect subscribers only

    As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 69 (2004)
    Issue (Month): 4 (October)
    Pages: 405-419

    as in new window
    Handle: RePEc:eee:stapro:v:69:y:2004:i:4:p:405-419

    Contact details of provider:
    Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description

    Order Information:
    Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
    Web: https://shop.elsevier.com/order?id=505573&ref=505573_01_ooc_1&version=01

    Related research

    Keywords: Long-range dependence Fractional Brownian motion Sub-fractional Brownian motion Occupation time fluctuations Branching systems;

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Deuschel, Jean-Dominique & Wang, Kongming, 1994. "Large deviations for the occupation time functional of a Poisson system of independent Brownian particles," Stochastic Processes and their Applications, Elsevier, vol. 52(2), pages 183-209, August.
    2. Bojdecki, Tomasz & Gorostiza, Luis G., 1999. "Fractional Brownian motion via fractional Laplacian," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 107-108, August.
    3. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Case of Long-Range Dependence," RePAd Working Paper Series lrsp-TRS402, Département des sciences administratives, UQO.
    Full references (including those not matched with items on IDEAS)

    Citations

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

    Cited by:
    1. Yan, Litan & Shen, Guangjun, 2010. "On the collision local time of sub-fractional Brownian motions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 296-308, March.
    2. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Cases of Large and Critical Dimensions," RePAd Working Paper Series lrsp-TRS404, Département des sciences administratives, UQO.
    3. Swanson, Jason, 2011. "Fluctuations of the empirical quantiles of independent Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 479-514, March.
    4. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2004. "Functional Limit Theorems for Occupation Time Fluctuations of Branching Systems in the Case of Long-Range Dependence," RePAd Working Paper Series lrsp-TRS402, Département des sciences administratives, UQO.
    5. Harnett, Daniel & Nualart, David, 2012. "Weak convergence of the Stratonovich integral with respect to a class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3460-3505.
    6. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2005. "A Long Range Dependence Stable Process and an Infinite Variance Branching System," RePAd Working Paper Series lrsp-TRS425, Département des sciences administratives, UQO.
    7. Slominski, Leszek & Ziemkiewicz, Bartosz, 2009. "On weak approximations of integrals with respect to fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 543-552, February.
    8. Luis G. Gorostiza & Reyla A. Navarro & Eliane R. Rodrigues, 2004. "Some Long-Range Dependence Processes Arising from Fluctuations of Particle Systems," RePAd Working Paper Series lrsp-TRS401, Département des sciences administratives, UQO.
    9. Tudor, Constantin, 2008. "Inner product spaces of integrands associated to subfractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2201-2209, October.
    10. Shen, Guangjun & Chen, Chao, 2012. "Stochastic integration with respect to the sub-fractional Brownian motion with H∈(0,12)," Statistics & Probability Letters, Elsevier, vol. 82(2), pages 240-251.
    11. Bojdecki, Tomasz & Talarczyk, Anna, 2012. "Particle picture interpretation of some Gaussian processes related to fractional Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 122(5), pages 2134-2154.

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:69:y:2004:i:4:p:405-419. 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: (Zhang, Lei).

    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.