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Optimal decision procedures for finite Markov chains. Part II: Communicating systems

Published online by Cambridge University Press:  01 July 2016

John Bather
John Bather*
Affiliation:
University of Sussex
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Abstract

A Markov process in discrete time with a finite state space is controlled by choosing the transition probabilities from a given convex family of distributions depending on the present state. The immediate cost is prescribed for each choice and it is required to minimise the average expected cost over an infinite future. The paper considers a special case of this general problem and provides the foundation for a general solution. The main result is that an optimal policy exists if each state of the system can be reached with positive probability from any other state by choosing a suitable policy.

Keywords

MARKOV CHAINDECISION PROCEDUREMINIMUM AVERAGE COSTOPTIMAL POLICYHOWARD MODELDYNAMIC PROGRAMMINGCONVEX DECISION SPACEACCESSIBILITY
Type
Research Article
Information
Advances in Applied Probability , Volume 5 , Issue 3 , December 1973 , pp. 521 - 540
Copyright
Copyright © Applied Probability Trust 1973 

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References

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