Hierarchical equilibria of branching populations

D. Dawson (), L. Gorostiza () and A. Wakolbinger ()
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D. Dawson: School of Mathematics and Statistics, Carleton University
L. Gorostiza: Centro de Investigacion y de Estudios Avanzados
A. Wakolbinger: Frankfurt am Main

No lrsp-TRS389, RePAd Working Paper Series from Département des sciences administratives, UQO

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.

Keywords: Multilevel branching; hierarchical mean-field limit; strong transience; genealogy. (search for similar items in EconPapers)
JEL-codes: C10 C40 (search for similar items in EconPapers)
Pages: 62 pages
Date: 2000-01-01
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