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On the construction problem for single-exit Markov chains

Published online by Cambridge University Press:  17 April 2009

P.K. Pollett
P.K. Pollett
Affiliation:
Department of Mathematics, The University of Queensland, Queensland 4072, Australia
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Abstract

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I shall consider the following problem: given a stable, conservative, single-exit q-matrix, Q, over an irreducible state-space S and a μ-subinvariant measure, m, for Q, determine all Q-processes for which m is a μ-invariant measure. I shall provide necessary and sufficient conditions for the existence and uniqueness of such a process.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 3 , June 1991 , pp. 439 - 450
Copyright
Copyright © Australian Mathematical Society 1991

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