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Sub-fractional Brownian motion and its relation to occupation times

Author

Listed:
  • 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)

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.

Suggested Citation

  • Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0132005
    as

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    File URL: http://www.repad.org/ca/on/lrsp/TRS376.pdf
    File Function: First version, 2004
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    References listed on IDEAS

    as
    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)

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    More about this item

    Keywords

    Long-range dependence; Fractional Brownian motion; Sub-fractional Brownian motion; Occupation time fluctuations; Branching systems.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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