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Exact distributions for reward functions on semi-Markov and Markov additive processes

Part of: Distribution theory - Probability Special processes

Published online by Cambridge University Press:  14 July 2016

Valeri T. Stefanov
Valeri T. Stefanov*
Affiliation:
The University of Western Australia
*
∗Postal address: School of Mathematics and Statistics, The University of Western Australia, Crawley, WA 6009, Australia. Email address: [email protected]
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Abstract

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The distribution theory for reward functions on semi-Markov processes has been of interest since the early 1960s. The relevant asymptotic distribution theory has been satisfactorily developed. On the other hand, it has been noticed that it is difficult to find exact distribution results which lead to the effective computation of such distributions. Note that there is no satisfactory exact distribution result for rewards accumulated over deterministic time intervals [0, t], even in the special case of continuous-time Markov chains. The present paper provides neat general results which lead to explicit closed-form expressions for the relevant Laplace transforms of general reward functions on semi-Markov and Markov additive processes.

Keywords

Semi-Markov processreward functionLaplace transformstopping timeexponential family

MSC classification

Primary: 60K15: Markov renewal processes, semi-Markov processes
Secondary: 60E10: Characteristic functions; other transforms
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1053 - 1065
Copyright
© Applied Probability Trust 2006 

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