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On the identification of continuous-time Markov chains with a given invariant measure

Part of: Markov processes

Published online by Cambridge University Press:  14 July 2016

P. K. Pollett
P. K. Pollett*
Affiliation:
The University of Queensland
*
∗Postal address: Department of Mathematics, The University of Queensland, QLD 4072, Australia. e-mail: pkp@maths.uq.oz.au
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Abstract

In [14] a necessary and sufficient condition was obtained for there to exist uniquely a Q-process with a specified invariant measure, under the assumption that Q is a stable, conservative, single-exit matrix. The purpose of this note is to demonstrate that, for an arbitrary stable and conservative q-matrix, the same condition suffices for the existence of a suitable Q-process, but that this process might not be unique. A range of examples is considered, including pure-birth processes, a birth process with catastrophes, birth-death processes and the Markov branching process with immigration.

Keywords

Q-PROCESSESSTATIONARY DISTRIBUTIONS

MSC classification

Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60J35: Transition functions, generators and resolvents 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)
Type
Research Article
Information
Journal of Applied Probability , Volume 31 , Issue 4 , December 1994 , pp. 897 - 910
Copyright
Copyright © Applied Probability Trust 1994 

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Footnotes

This work was funded under an Australian Research Council Grant and a University of Queensland Special Project Grant.

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