Hierarchical equilibria of branching populations
| dc.creator | Dawson, D. A. | |
| dc.creator | Gorostiza, L. G. | |
| dc.creator | Wakolbinger, A. | |
| dc.date | 2003-10-15 | |
| dc.date.accessioned | 2026-07-07T05:01:56Z | |
| dc.date.available | 2026-07-07T05:01:56Z | |
| dc.description | The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group $Ω_N$ 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. | |
| dc.description | 62 pages | |
| dc.identifier | https://arxiv.org/abs/math/0310229 | |
| dc.identifier | http://arxiv.org/abs/math/0310229 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68865 | |
| dc.subject | Probability | |
| dc.subject | Populations and Evolution | |
| dc.subject | 60J80;60J60,60G60 | |
| dc.title | Hierarchical equilibria of branching populations | |
| dc.type | text |