The life spans of a Bellman-Harris branching process with immigration
type: Item
instance of: scholarly article
title: The life spans of a Bellman-Harris branching process with immigration
zbMATH Open document ID: 0668.60076
DOI: 10.1007/BF01093821
author: I. S. Badalbaev
author: A. Mashrabbaev
published in: Journal of Soviet Mathematics
publication date: 1987-01-01T00:00:00Z
review text: [For the entire collection see Zbl 0626.00025.] One considers two schemes of the Bellman-Harris process with immigration when a) the lifetime of the particles is an integral-valued random variable and the immigration is defined by a sequence of independent random variables; b) the distribution of the lifetime of the particles is nonlattice and the immigration is a process with continuous time. One investigates the properties of the life spans of such processes. The results obtained here are a generalization to the case of Bellman-Harris processes of the results of \textit{A. M. Zubkov} [Theory Probab. Appl. 17, 174-183 (1972; Zbl 0267.60084); translation from Teor. Veroyatn. Primen. 17, 179-188 (1972)] obtained for Markov branching processes. For the proof one makes use in an essential manner of the well-known Goldstein inequalities estimating the generating function of the Bellman-Harris process in terms of the generating functions of the imbedded Galton- Watson process.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 4094539
zbMATH Keywords: Bellman-Harris process with immigration
zbMATH Keywords: Galton-Watson process
MaRDI profile type: Publication
cites work: On the critical Galton-Watson process with immigration
cites work: Q5674726
cites work: Life-Periods of a Branching Process with Immigration
cites work: Discrete Limit Distributions of the Number of Particles in Critical Bellman–Harris Branching Process
cites work: Q4085018
cites work: Q5512461
description: scientific article; zbMATH DE number 4094539