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Sub-fractional Brownian motion and its relation to occupation times

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  • Tomasz Bojdecki

    ()
    (Institute of Mathematics, University of Warsaw)

  • Luis G. Gorostiza

    ()
    (Department of Mathematics, Centro de Investigacion y de Estudios Avanzados)

  • Anna Talarczyk

    ()
    (Institute of Mathematics, University of Warsaw)

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    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 E (0, 2), we show how it arises from occupation time fluctuations of branching particle systems for h >= 1 and we exhibit the long memory effect of the initial condition.

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    File URL: http://www.repad.org/ca/on/lrsp/TRS376.pdf
    File Function: First version, 2004
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    Bibliographic Info

    Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS376.

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    Length: 14 pages
    Date of creation: 15 Jun 2004
    Date of revision:
    Handle: RePEc:pqs:wpaper:0132005

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    Related research

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

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    References

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    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.
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    Cited by:
    1. 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.
    2. 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.
    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, 2005. "A Long Range Dependence Stable Process and an Infinite Variance Branching System," RePAd Working Paper Series lrsp-TRS425, Département des sciences administratives, UQO.
    5. 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.

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