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Invariant Probabilities with Geometric Tail

Published online by Cambridge University Press:  27 July 2009

Jean B. Lasserre  and
Henk Tijms
Jean B. Lasserre
Affiliation:
LAAS-CNRS, 7 Avenue du Colonel Roche, 31077 Toulouse Cédex, France
Henk Tijms
Affiliation:
Department of Econometrics, Vrije Universiteit, 1081 HV Amsterdam, The Netherlands
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Abstract

We present necessary and suffi2ient Foster-type conditions for a countable state Markov chain to have an invariant probability with at least a geometric tail. These conditions are obtained by using a generalized Farkas Theorem in Linear Algebra. The purpose of this note is also to pose an interesting and important research problem that is still largely open.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 2 , April 1996 , pp. 213 - 221
Copyright
Copyright © Cambridge University Press 1996

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