Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction
type: Item
instance of: scholarly article
title: Uniqueness, extinction and explosivity of generalised Markov branching processes with pairwise interaction
zbMATH Open document ID: 1218.60070
author: Anyue Chen
author: Hanjun Zhang
author: P. K. Pollett
author: Junping Li
published in: Methodology and Computing in Applied Probability
publication date: 2010-10-14T00:00:00Z
review text: The paper deals with Markov branching processes with pairwise interaction. These processes are certain continuous-time Markov chains with state space \(\mathbb{Z}_{\geq 0}\). They are defined via their \(q\)-matrix \(Q\) which in turn is defined in terms of two sequences, \((b_n)_{n \geq 0}\) and \((w_n)_{n \geq 0}\). The former basically governs the branching law whereas the latter governs the degree of interaction. It is shown that if the \(q\)-matrix \(Q\) is essentially-explosive (a notion that is defined in the paper), then the process is honest iff the mean death rate is greater than or equal to the mean birth rate. In the sub-explosive regime, the process is shown to be honest except in special cases. Further, a uniqueness criterion is provided. Finally, extinction times and explosivity are investigated.
reviewed by: Matthias Meiners
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J27
zbMATH DE Number: 5800284
zbMATH Keywords: Markov branching process
zbMATH Keywords: pairwise interaction
zbMATH Keywords: extinction
zbMATH Keywords: explosion
zbMATH Keywords: regularity
MaRDI profile type: Publication
full work available at URL: s11009-009-9121-y
OpenAlex ID: W2080636546
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DOI: 10.1007/S11009-009-9121-Y
description: scientific article; zbMATH DE number 5800284