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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 {P m }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 P m 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

Information

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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