Markov branching processes regulated by emigration and large immigration
type: Item
instance of: scholarly article
title: Markov branching processes regulated by emigration and large immigration
zbMATH Open document ID: 0836.60078
DOI: 10.1016/0304-4149(94)00083-6
author: Anyue Chen
author: Eric Renshaw
published in: Stochastic Processes and their Applications
publication date: 1995-07-12T00:00:00Z
review text: Here is an informal description of the continuous-time Markov chain on the nonnegative integers discussed in this paper. From any state \(i > 0\) reproduction occurs according to a Markov branching process; in addition catastrophes, or mass emigrations, occur, causing the population to become extinct, at a rate which depends on \(i\). However there is immediate immigration into state 0, in the sense that transitions from there to state \(i\) occur at the rate \(\alpha_i\) where \(\sum \alpha_i = \infty\). Existence and uniqueness are discussed. Further properties, in particular positive recurrence, are derived for the special case where the emigration rate is proportional to \(i\). The methods are analytical. The interest of the work is primarily as study in general Markov chain theory. The fact that 0 is an instantaneous state means that sample path behaviour is rather wild for the model to serve as one for a population.
Mathematics Subject Classification ID: 60J27
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 772937
zbMATH Keywords: instantaneous state
zbMATH Keywords: Markov processes
zbMATH Keywords: immediate immigration
zbMATH Keywords: Markov chain
MaRDI profile type: Publication
full work available at URL: 0304-4149(94)00083-6
OpenAlex ID: W2054190048
cites work: Continuous-time Markov chains. An applications-oriented approach
cites work: Q3664178
cites work: Q5674726
cites work: Markov branching processes with instantaneous immigration
cites work: Recurrence of Markov branching processes with immigration
cites work: Existence and uniqueness criteria for conservative uni-instantaneous denumerable Markov processes
cites work: Q5524074
cites work: A Limit Theorem for a Branching Process with State-Dependent Immigration
cites work: Q5727090
cites work: Q3994575
cites work: Q3234866
cites work: A branching process with a state dependent immigration component
cites work: On the age distribution of a Markov chain
cites work: Absorbing Markov and branching processes with instantaneous resurrection
cites work: Modelling Biological Populations in Space and Time
cites work: Denumerable Markov processes and the associated contraction semigroups on l
cites work: Remarks on a Markov chain example of Kolmogorov
cites work: Some results on continuous time branching processes with state-dependent immigration
cites work: Q3999491
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description: scientific article; zbMATH DE number 772937