An efficient procedure for computing quasistationary distributions of Markov chains with sparse transition structure

Phil Pollett and David Stewart

Abstract: We shall describe a computational procedure for evaluating the quasistationary distributions of a continuous-time Markov chain. Our method, which is an "iterative version" of Arnoldi's algorithm, is appropriate for dealing with cases where the matrix of transition rates is large and sparse, but does not exhibit a banded structure which might otherwise be usefully exploited. We shall illustrate the method with reference to an epidemic model and we shall compare the computed quasistationary distribution with an appropriate diffusion approximation.

AMS 1991 Subject Classification: 60J27; 65F15.

Keywords: Markov chains; quasistationary distributions; Arnoldi algorithm.

Acknowledgement: This worked was funded by the Australian Research Council and the University of Queensland.

The authors:

• Phil Pollett, Discipline of Mathematics, The University of Queensland. pkp@maths.uq.edu.au
• David Stewart, Programme in Advanced Computation, School of Mathematical Sciences, The Australian National University. Present address: Department of Mathematics, Virginia Tech. stewart@math.vt.edu

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Last modified: 26th December 1995