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Approximating the Stationary Distribution of an Infinite Stochastic Matrix
Daniel P. Heyman
Journal of Applied Probability
Vol. 28, No. 1 (Mar., 1991), pp. 96-103
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3214743
Page Count: 8
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We are given a Markov chain with states 0, 1, 2,…. We want to get a numerical approximation of the steady-state balance equations. To do this, we truncate the chain, keeping the first n states, make the resulting matrix stochastic in some convenient way, and solve the finite system. The purpose of this paper is to provide some sufficient conditions that imply that as n tends to infinity, the stationary distributions of the truncated chains converge to the stationary distribution of the given chain. Our approach is completely probabilistic, and our conditions are given in probabilistic terms. We illustrate how to verify these conditions with five examples.
Journal of Applied Probability © 1991 Applied Probability Trust