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The asymptotic behaviour of the minimal total expected cost for the denumerable state Markov decision model

Published online by Cambridge University Press:  14 July 2016

Arie Hordijk ,
Paul J. Schweitzer  and
Henk Tijms
Arie Hordijk
Affiliation:
Mathematisch Centrum, Amsterdam
Paul J. Schweitzer
Affiliation:
IBM Thomas J. Watson Research Center, Yorktown Heights, New York
Henk Tijms
Affiliation:
Mathematisch Centrum, Amsterdam
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Abstract

This paper considers the discrete time Markov decision model with a denumerable state space and finite action space. Under certain conditions it is proved that the minimal total expected cost for a planning horizon of n epochs minus n times the minimal long-run average expected cost per unit time has a finite limit as n → ∞ for each initial state.

Keywords

MARKOV DECISION THEORYDENUMERABLE STATE SPACEMINIMAL AVERAGE COSTMINIMAL TOTAL COSTLIMITING BEHAVIOUR
Type
Research Papers
Information
Journal of Applied Probability , Volume 12 , Issue 2 , June 1975 , pp. 298 - 305
Copyright
Copyright © Applied Probability Trust 1975 

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