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Zbl 0721.60070
Heyman, Daniel P.
Approximating the stationary distribution of an infinite stochastic matrix. (English)
[J] J. Appl. Probab. 28, No.1, 96-103 (1991). ISSN 0021-9002

Summary: 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.

MSC 2000:: *60J10 Markov chains with discrete parameter
65C99 Numerical simulation

Keywords: Hessenberg matrices; numerical approximation; steady-state balance equations; stationary distributions

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