Geometric growth in near-supercritical population size dependent multitype Galton-Watson processes
type: Item
instance of: scholarly article
title: Geometric growth in near-supercritical population size dependent multitype Galton-Watson processes
zbMATH Open document ID: 0694.60079
author: Fima Klebaner
published in: The Annals of Probability
publication date: 1989-01-01T00:00:00Z
review text: A population process with finitely many types is considered in which the branching property holds except that the offspring distributions depend upon the current population size. It is shown that if the mean matrix of offspring distributions converges, as the population size becomes large, to that of a supercritical branching process, then the asymptotic growth of the process essentially mimics that of the ``limit'' branching process in its geometric growth. For mean square normed convergence, conditions on the variances are required. Some sufficient conditions for geometric growth are also stated and proved. The paper generalizes results for one-type processes given by the author [J. Appl. Probab. 21, 40-49 (1984; Zbl 0544.60073)].
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J05
zbMATH DE Number: 4137149
zbMATH Keywords: multidimensional Markov chains
zbMATH Keywords: growth rates
zbMATH Keywords: population process
zbMATH Keywords: supercritical branching process
zbMATH Keywords: geometric growth
reviewed by: D. R. Grey
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176991167
OpenAlex ID: W2004997961
DOI: 10.1214/AOP/1176991167
description: scientific article; zbMATH DE number 4137149