TY  - JOUR
A1  - Dawson, Donald A.
A1  - Gorostiza, Luis G.
A1  - Wakolbinger, Anton
T1  - Hierarchical equilibria of branching populations
T2  - Electronic journal of probability
N2  - 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.
KW  - multilevel branching
KW  - hierarchical mean-field limit
KW  - strong transience
KW  - genealogy
Y1  - 2004
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/32889
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-328898
SN  - 1083-6489
N1  - This work is licensed under a Creative Commons Attribution 3.0 License http://creativecommons.org/licenses/by/3.0/ .
VL  - 9
SP  - 316
EP  - 381
PB  - EMIS ELibEMS
CY  - [Madralin]
ER  -