Direct analytical methods for determining quasistationary distributions for continuous-time Markov chains

A.G. Hart and P.K. Pollett

Abstract: We shall be concerned with the problem of determining the quasistationary distributions of an absorbing continuous-time Markov chain directly from the transition-rate matrix Q. We shall present conditions which ensure that any finite \mu-invariant probability measure for Q is a quasistationary distribution. Our results will be illustrated with reference to birth and death processes.

AMS 1991 Subject Classification: 60J27.

Keywords: Markov chains; invariant measures.

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

The authors:

• Andrew Hart, Discipline of Mathematics, The University of Queensland. agh@maths.uq.edu.au
• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au

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Last modified: 26th December 1995