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Occupation Time Fluctuations of an Infinite Variance Branching System in Large Dimensions

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 limit theorems for rescaled occupation time fluctuations of a (d, , )-branching particle system (particles moving in Rd according to a spherically symmetric -stable L´evy process, (1 + )- branching, 0 (1 + )/ . The fluctuation processes are continuous but their limits are stable processes with independent increments, which have jumps. The convergence is in the sense of finite-dimensional distributions, and also of space-time random fields (tightness does not hold in the usual Skorohod topology). The results are in sharp contrast with those for intermediate dimensions, /

Suggested Citation

  • 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.
  • Handle: RePEc:pqs:wpaper:112006
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    File URL: http://www.repad.org/ca/on/lrsp/TRS426.pdf
    File Function: First version, 2005
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    Cited by:

    1. 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.

    More about this item

    Keywords

    Branching particle system; critical and large dimensions; limit theorem; occupation time fluctuation; stable process.;
    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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