Geometric growth for stochastic difference equations with application to branching populations
type: Item
instance of: scholarly article
title: Geometric growth for stochastic difference equations with application to branching populations
zbMATH Open document ID: 1151.60037
author: Manuel Molina
author: Miguel González
author: Inés M. del Puerto
published in: Bernoulli
publication date: 2007-05-24T00:00:00Z
review text: The article considers the asymptotic growth rate for an integer-valued random process given by a stochastic difference equation driven by a martingale difference sequence. Under certain technical conditions, a suitably normalized version of this process is shown to converge in \(\alpha\)th mean for a certain \(\alpha\in[1, 2]\) to a nonnegative random variable, which is strictly positive if and only if the process under consideration explodes. Under an additional condition, this in turn leads to a result that implies in particular geometric growth on the explosion set. The results are applied to asexual controlled branching processes with random control functions and bisexual branching processes.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 5156988
zbMATH Keywords: stochastic difference equation
zbMATH Keywords: geometric growth
zbMATH Keywords: brancking processes
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3150/bj/1161614953
OpenAlex ID: W2000821025
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DOI: 10.3150/BJ/1161614953
description: scientific article; zbMATH DE number 5156988