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Semi-Markov and reward fields

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  • Soltani, A.R.
  • Ghasemi, H.

Abstract

We introduce semi-Markov fields and provide formulations for the basic terms in the semi-Markov theory. In particular we define and consider a class of associated reward fields. Then we present a formula for the expected reward at any multidimensional time epoch. The formula is indeed new even for the classical semi-Markov processes. It gives the expected cumulative reward for fairly large classes of reward functions; in particular, it provides the formulas for the expected cumulative reward given in Masuda and Sumitau (1991), Soltani (1996) and Soltani and Khorshidian (1998).

Suggested Citation

  • Soltani, A.R. & Ghasemi, H., 2014. "Semi-Markov and reward fields," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 71-76.
    • Handle: RePEc:eee:stapro:v:95:y:2014:i:c:p:71-76
    DOI: 10.1016/j.spl.2014.08.012
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    1. Erhan Çinlar, 1975. "Exceptional Paper--Markov Renewal Theory: A Survey," Management Science, INFORMS, vol. 21(7), pages 727-752, March.
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    Cited by:

    1. Karamzadeh, M. & Soltani, A.R. & Mardani-Fard, H.A., 2020. "On a class of spatial renewal processes: Renewal processes synchronization probabilities," Statistics & Probability Letters, Elsevier, vol. 158(C).

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