Further results on the relationship between m-invariant measures and quasistationary distributions for absorbing continuous-time Markov chains

Sylvia Elmes, Phil Pollett and David Walker

Abstract: This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on m-invariant and m-subinvariant measures where absorption occurs with probability less than 1. In particular, the well known premise that the m-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between m-invariant measures and quasistationary distributions is discussed.

AMS 1991 Subject Classification: 60J27; 60J35.

Keywords: Invariant measures; Q-processes.

Acknowledgement: This worked was funded by the Australian Research Council.

The authors:

• Sylvia Elmes, Faculty of Environmental Sciences, Griffith University. S.Elmes@ens.gu.edu.au
• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au
• David Walker, Discipline of Mathematics, The University of Queensland. dmw@maths.uq.edu.au

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Last modified: 12th March 1996