Hierarchical equilibria of branching populations
Electronic Journal of Probability , Volume 9 p. 316- 381
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 Bℓ (N) 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.
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