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Wed, 29 Jan 2014 16:22:58 +0100Wed, 29 Jan 2014 16:22:58 +0100Hierarchical equilibria of branching populations
http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32889
The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group ΩN 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→∞ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls B(N)ℓ of hierarchical radius ℓ 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.Donald A. Dawson; Luis G. Gorostiza; Anton Wakolbingerarticlehttp://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32889Wed, 29 Jan 2014 16:22:58 +0100