Approximations of quasistationary distributions for Markov chains

L.A. Breyer and A.G. Hart

Abstract: We consider a simple and widely used method for evaluating quasistationary distributions of continuous time Markov chains. The infinite state space is replaced by a large, but finite approximation, which is used to evaluate a candidate distribution.

We give some conditions under which the method works, and describe some important pitfalls.

AMS 1991 Subject Classification: 60J27.

Keywords: mu-subinvariant measures; conditioned processes; limiting conditional distributions.

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

The authors:

• Laird Breyer, Discipline of Mathematics, The University of Queensland. lab@maths.uq.edu.au
• Andrew Hart, Discipline of Mathematics, The University of Queensland. agh@maths.uq.edu.au

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Last modified: 27th April 1997