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Ergodicity and stability of generalised Markov branching processes with resurrection

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

Anyue Chen
Anyue Chen*
Affiliation:
University of Greenwich
*
∗ Postal address: School of Computing and Mathematical Sciences, University of Greenwich, Maritime Greenwich Campus, Old Royal Naval College, Park Row, Greenwich, London SE10 9LS, UK. Email address: a.chen@greenwich.ac.uk
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Abstract

This paper concentrates on investigating ergodicity and stability for generalised Markov branching processes with resurrection. Easy checking criteria including several clear-cut corollaries are established for ordinary and strong ergodicity of such processes. The equilibrium distribution is given in an elegant closed form for the ergodic case. The probabilistic interpretation of the results is clear and thus explained.

Keywords

Ordinary ergodicitystrong ergodicityequilibrium distributionMarkov branching processesgeneralised Markov branching processes with resurrection

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 4 , December 2002 , pp. 786 - 803
Copyright
Copyright © Applied Probability Trust 2002 

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