An Efficient Procedure for Computing Quasi-Stationary Distributions of Markov Chains by Sparse Transition Structure

We describe a computational procedure for evaluating the quasi-stationary 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 illustrate the method with reference to an epidemic model and we compare the computed quasi-stationary distribution with an appropriate diffusion approximation.