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Approximation of the invariant probability measure of an infinite stochastic matrix

Published online by Cambridge University Press:  01 July 2016

D. Wolf
D. Wolf*
Affiliation:
Technische Universität München
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Abstract

Let P denote an irreducible positive recurrent infinite stochastic matrix with the unique invariant probability measure π. We consider sequences {Pm}m∊N of stochastic matrices converging to P (pointwise), such that every Pm has at least one invariant probability measure πm. The aim of this paper is to find conditions, which assure that at least one of sequences {πm}m∊N converges to π (pointwise). This includes the case where the Pm are finite matrices, which is of special interest. It is shown that there is a sequence of finite stochastic matrices, which can easily be constructed, such that {πm}m∊N converges to π. The conditions given for the general case are closely related to Foster's condition.

Keywords

STOCHASTIC MATRICESINVARIANT PROBABILITY MEASURESAPPROXIMATIONFOSTER'S CONDITIONPOTENTIALS
Type
Research Article
Information
Advances in Applied Probability , Volume 12 , Issue 3 , September 1980 , pp. 710 - 726
Copyright
Copyright © Applied Probability Trust 1980 

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