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1 results

  • Approximating the stationary distribution of an infinite stochastic matrix

  • Daniel P. Heyman
  • Journal:
    Journal of Applied Probability / Volume 28 / Issue 1 / March 1991
    Published online by Cambridge University Press:
    14 July 2016, pp. 96-103
    Print publication:
    March 1991

  • 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.