Critical branching processes with nonhomogeneous migration
type: Item
instance of: scholarly article
title: Critical branching processes with nonhomogeneous migration
zbMATH Open document ID: 0576.60077
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: A Galton-Watson branching process is modified in the following way: at generation n, there is probability \(p_ n\) that just one of the individuals present (if any) is eliminated before reproduction; probability \(r_ n\) that, in addition to reproduction, immigration occurs according to some specified (time-homogeneous) distribution with mean m; and probability \(q_ n\) that reproduction occurs in the standard way, where \(p_ n+q_ n+r_ n=1\). In the critical case with \(p_ n=mr_ n\) and \(p_ n\) converging to zero in regularly varying fashion, conditional limit theorems for the population size are obtained.
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 92D10
Mathematics Subject Classification ID: 60J85
Mathematics Subject Classification ID: 92D25
zbMATH DE Number: 3921672
zbMATH Keywords: decreasing random migration
zbMATH Keywords: Galton-Watson branching process
zbMATH Keywords: immigration
zbMATH Keywords: conditional limit theorems
author: Nikolay M. Yanev
author: K. V. Mitov
reviewed by: D. R. Grey
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176992914
OpenAlex ID: W1982001851
DOI: 10.1214/AOP/1176992914
Recommended article: Q4840714
Recommended article: Q4350393
Recommended article: Q4810566
Recommended article: Q3746628
Recommended article: Critical Markov Branching Processes with Non-homogeneous Poisson Immigration
Recommended article: Q4630703
Recommended article: Q3497003
Recommended article: Q4013641
Recommended article: Lifetimes of Critical Branching Processes with Random Migration
description: scientific article; zbMATH DE number 3921672