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A Long Range Dependence Stable Process and an Infinite Variance Branching System

Author

Listed:
  • T. Bojdecki

    (Institute of Mathematics, University of Warsaw)

  • Luis G. Gorostiza

    (Departamento de Mathematicas, Centro de Investigacion y de Estudios Avanzados, LRSP)

  • A. Talarczyk

    (Institute of Mathematics, University of Warsaw)

Abstract

We prove a functional limit theorem for the rescaled occupation time fluctuations of a (d, , )- branching particle system (particles moving in Rd according to a symmetric -stable L´evy process, branching law in the domain of attraction of a (1 + )-stable law, 0 d/(d + ), which coincides with the case of finite variance branching ( = 1), and another one for d/(d + ), where the long range dependence depends on the value of . The long range dependence is characterized by a dependence exponent which describes the asymptotic behavior of the codi erence of increments of on intervals far apart, and which is d/ for the first case and (1 + - d/(d + ))d/ for the second one. The convergence proofs use techniques of S0(Rd)-valued processes.

Suggested Citation

  • 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.
    • Handle: RePEc:pqs:wpaper:102006
    as

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    File URL: http://www.repad.org/ca/on/lrsp/TRS425.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    3. 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.
    4. T. Bojdecki & Luis G. Gorostiza & A. Talarczyk, 2005. "Occupation Time Fluctuations of an Infinite Variance Branching System in Large Dimensions," RePAd Working Paper Series lrsp-TRS426, Département des sciences administratives, UQO.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Branching particle system; occupation time fluctuation; functional limit theorem; stable process; long range dependence.;
    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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