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Regularity and reversibility results for birth-death-migration processes

Part of: Markov processes Special processes

Published online by Cambridge University Press:  14 July 2016

Eric Renshaw  and
Yonglong Dai
Eric Renshaw*
Affiliation:
Strathclyde University
Yonglong Dai*
Affiliation:
Zhongshan University
*
∗Postal address: Department of Statistics and Modelling Science, Strathclyde University, Livingstone Tower, 26 Richmond Street, Glasgow Gl 1XH, UK.
∗∗Postal address: Department of Mathematics, Zhongshan University, Guangzhou, 510275, China.
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Abstract

A spatial process is considered in which two general birth-death processes are linked by migration of individuals. We examine conditions for weak symmetry and regularity, and develop necessary and sufficient conditions for recurrence. The results are easily extended to the k-process case.

Keywords

BIRTH-DEATHMIGRATIONMARKOV CHAINSREGULARITYSYMMETRYRECURRENCE

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60K25: Queueing theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 3 , September 1997 , pp. 685 - 697
Copyright
Copyright © Applied Probability Trust 1997 

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