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On sets of countable non-negative matrices and Markov decision processes

Published online by Cambridge University Press:  01 July 2016

Douglas P. Kennedy
Douglas P. Kennedy*
Affiliation:
University of Cambridge
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Abstract

Consider a set S of countable non-negative matrices satisfying the property that for any two indices i, j, for some n ≧ 1 there are matrices M1, M2, · · ·, Mn in S with (M1M2 · · · Mn)ij >0. For non-negative vectors x set Tx = supM∈SMx, where the supremum is taken separately in each coordinate. Assume that for each x with Tx finite in each coordinate there is a matrix in S which achieves the supremum simultaneously for all coordinates. With these two assumptions on S, the R-theory for a countable irreducible matrix is extended to the operator T. The results are used to consider the existence of stationary optimal policies for Markov decision processes with multiplicative rewards.

Keywords

NON-NEGATIVE MATRICESR-THEORYPERRON–FROBENIUS THEORYDYNAMIC PROGRAMMINGMARKOV DECISION PROCESSES
Type
Research Article
Information
Advances in Applied Probability , Volume 10 , Issue 3 , September 1978 , pp. 633 - 646
Copyright
Copyright © Applied Probability Trust 1978 

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References

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