Exact Distributions for Reward Functions on Semi-Markov and Markov Additive Processes

Valeri Stefanov

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    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.
    Original languageEnglish
    Pages (from-to)1053-1065
    JournalJournal of Applied Probability
    Volume43
    Issue number4
    DOIs
    Publication statusPublished - 2006

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