Limiting distributions and regeneration times for multitype branching processes with immigration in a random environment
type: Item
instance of: scholarly article
title: Limiting distributions and regeneration times for multitype branching processes with immigration in a random environment
zbMATH Open document ID: 0623.60090
published in: The Annals of Probability
publication date: 1987-01-01T00:00:00Z
review text: This article studies sufficient conditions for the existence of a limiting distribution for a multitype branching process (Z(t)) in a random environment. The work extends results by Kaplan, Athreya and Karlin, and Tanny. Another parallel is drawn to the results of Kesten, Kozlov and Spitzer using branching processes with immigration in a random environment as a tool to find limiting distributions for random walks in a random environment. Special interest is given to sufficient criteria for the survival distribution to decrease exponentially fast. Here the environment has to be an i.i.d. sequence.
Mathematics Subject Classification ID: 60J10
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60G50
zbMATH DE Number: 4011600
zbMATH Keywords: multitype branching process
zbMATH Keywords: branching processes with immigration
zbMATH Keywords: random environment
zbMATH Keywords: survival distribution
author: Eric S. Key
reviewed by: F. Thomas Bruss
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992273
OpenAlex ID: W2059582497
DOI: 10.1214/AOP/1176992273
description: scientific article; zbMATH DE number 4011600