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Markov population replacement processes

Part of: Markov processes Special processes

Published online by Cambridge University Press:  01 July 2016

Ioannis I. Gerontidis
Ioannis I. Gerontidis*
Affiliation:
University of Thessaloniki
*
* Postal address: Mathematics Department, University of Thessaloniki, 54006 Thessaloniki, Greece.
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Abstract

We consider a migration process whose singleton process is a time-dependent Markov replacement process. For the singleton process, which may be treated as either open or closed, we study the limiting distribution, the distribution of the time to replacement and related quantities. For a replacement process in equilibrium we obtain a version of Little's law and we provide conditions for reversibility. For the resulting linear population process we characterize exponential ergodicity for two types of environmental behaviour, i.e. either convergent or cyclic, and finally for large population sizes a diffusion approximation analysis is provided.

Keywords

CONVERGENCE RATESDIFFUSION APPROXIMATIONDYNAMIC EQUILIBRIUMPARTIAL BALANCEQUASI-REVERSIBILITYSTOCHASTIC NETWORKWHITTLE PROCESS

MSC classification

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Secondary: 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 3 , September 1995 , pp. 711 - 740
Copyright
Copyright © Applied Probability Trust 1995 

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