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Hierarchical equilibria of branching populations

  • 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)

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    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.

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    File URL: http://www.repad.org/ca/on/lrsp/TRS389.pdf
    File Function: First version, 2000
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    Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number lrsp-TRS389.

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    Length: 62 pages
    Date of creation: 01 Jan 2000
    Date of revision:
    Handle: RePEc:pqs:wpaper:0162005
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    1. Durrett, R., 1978. "The genealogy of critical branching processes," Stochastic Processes and their Applications, Elsevier, vol. 8(1), pages 101-116, November.
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