| Título: | Hierarchical Equilibria of Branching Populations |
| Autores: |
Dawson, Donald A.; Carleton University Gorostiza, Luis G.; Centro de Investigacion y de Estudios Avanzados, Mexico D.F., Mexico Wakolbinger, Anton; Goethe Universitat, Frankfurt am Main, Germany |
| Fecha: | 2004-01-01 |
| Publicador: | Electronic Journal of Probability |
| Fuente: |
Ver documento |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Multilevel branching, hierarchical mean-field limit, strong transience, genealogy Primary 60J80; Secondary 60J60, 60G60 |
| Descripción: | 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. |
| Idioma: | No aplica |
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