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2004 Hierarchical Equilibria of Branching Populations
Donald Dawson, Luis Gorostiza, Anton Wakolbinger
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Electron. J. Probab. 9: 316-381 (2004). DOI: 10.1214/EJP.v9-200


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 $N\to\infty$ (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.


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Donald Dawson. Luis Gorostiza. Anton Wakolbinger. "Hierarchical Equilibria of Branching Populations." Electron. J. Probab. 9 316 - 381, 2004.


Accepted: 2 April 2004; Published: 2004
First available in Project Euclid: 6 June 2016

zbMATH: 1076.60073
MathSciNet: MR2080603
Digital Object Identifier: 10.1214/EJP.v9-200

Primary: 60J80
Secondary: 60G60, 60J60


Vol.9 • 2004
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