Hierarchical Equilibria of Branching Populations
Donald A. Dawson, Carleton University
Luis G. Gorostiza, Centro de Investigacion y de Estudios Avanzados, Mexico D.F., Mexico
Anton Wakolbinger, Goethe Universitat, Frankfurt am Main, Germany
Abstract
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 $Ntoinfty$ (called the {em 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.
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.