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Hierarchical equilibria of branching populations

Author

Listed:
  • D.A. Dawson

    (School of Mathematics and Statistics, Carleton University)

  • L.G. Gorostiza

    (Centro de Investigacion y de Estudios Avanzados)

  • A. Wakolbinger

    (Frankfurt am Main)

Abstract

The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group (Omega)N consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit N -> (infinity symbol) (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls (symbole)(N) of hierarchical radius (symbol) converge to a backward Markov chain on R+. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.

Suggested Citation

  • D.A. Dawson & L.G. Gorostiza & A. Wakolbinger, 2000. "Hierarchical equilibria of branching populations," RePAd Working Paper Series lrsp-TRS389, Département des sciences administratives, UQO.
    • Handle: RePEc:pqs:wpaper:0162005
    as

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    File URL: http://www.repad.org/ca/on/lrsp/TRS389.pdf
    File Function: First version, 2000
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    References listed on IDEAS

    as
    1. Durrett, R., 1978. "The genealogy of critical branching processes," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 101-116, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multilevel branching; hierarchical mean-field limit; strong transience; genealogy.;
    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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