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Hierarchical equilibria of branching populations | | D.A. Dawson
; L.G. Gorostiza
; A. Wakolbinger
; | | Date: |
15 Oct 2003 | | Subject: | Probability; Populations and Evolution MSC-class: 60J80;60J60,60G60 | math.PR q-bio.PE | | 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 $N oinfty$ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls $B^{(N)}_ell$ of hierarchical radius $ell$ converge to a backward Markov chain on $mathbb{R_+}$. 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. | | Source: | arXiv, math.PR/0310229 | | Services: | Forum | Review | PDF | Favorites | |
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