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.
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Publisher Info
Paper provided by Département des sciences administratives, UQO in its series RePAd Working Paper Series with number
lrsp-TRS389.
Length: 62 pages Date of creation: 01 Jan 2000 Date of revision: Handle: RePEc:pqs:wpaper:0162005
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Find related papers by JEL classification: C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - General C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General