Uniqueness and extinction properties of generalised Markov branching processes
type: Item
instance of: scholarly article
title: Uniqueness and extinction properties of generalised Markov branching processes
zbMATH Open document ID: 1010.60076
DOI: 10.1016/S0022-247X(02)00251-2
author: Anyue Chen
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: If in a continuous-time Galton-Watson process branching of a particle occurs with rate \(r> 0\), and the system is in the state \(i\), then the next branching event occurs with rate \(ir\). \textit{R.-R. Chen} [J. Appl. Probab. 34, No. 1, 14-23 (1997; Zbl 0874.60078)] discussed a generalization of this classical model by assuming that for a fixed number \(\nu> 0\) the next branching event occurs with rate \(i^\nu r\) instead, for all \(i\geq 0\). In the present paper it is shown that this leads to a unique process. Extinction properties are also studied.
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 1866640
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1866640