Hierarchical equilibria of branching populations

  • 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 B(N)ℓ 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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Metadaten
Author:Donald A. Dawson, Luis G. Gorostiza, Anton WakolbingerGND
URN:urn:nbn:de:hebis:30:3-328898
DOI:https://doi.org/10.1214/EJP.v9-200
ISSN:1083-6489
Parent Title (English):Electronic journal of probability
Publisher:EMIS ELibEMS
Place of publication:[Madralin]
Document Type:Article
Language:English
Year of Completion:2014
Date of first Publication:2004/04/26
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2014/01/29
Tag:genealogy; hierarchical mean-field limit; multilevel branching; strong transience
Volume:9
Page Number:66
First Page:316
Last Page:381
Note:
This work is licensed under a Creative Commons Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/ .
HeBIS-PPN:363696105
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Gxx Stochastic processes / 60G60 Random fields
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
Sammlungen:Universitätspublikationen
Licence (German):License LogoCreative Commons - Namensnennung 3.0

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