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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
DOI: 10.2307/3214743
Stable URL: http://www.jstor.org/stable/3214743
Page Count: 8
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Approximating the Stationary Distribution of an Infinite Stochastic Matrix
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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.

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