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Approximating the stationary distribution of an infinite stochastic matrix

Published online by Cambridge University Press:  14 July 2016

Daniel P. Heyman
Daniel P. Heyman*
Affiliation:
Bellcore
*
∗Postal address: Bellcore, Room 3D-308, 331 Newman Springs Road, Red Bank, NJ 07701, USA.
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Abstract

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.

Keywords

MARKOV CHAINSTRUNCATIONAUGMENTATIONHESSENBERG MATRICES
Type
Research Papers
Information
Journal of Applied Probability , Volume 28 , Issue 1 , March 1991 , pp. 96 - 103
Copyright
Copyright © Applied Probability Trust 1991 

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