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Maximal success durations for a semi-Markov process

Author

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  • Fousler, David E.
  • Karlin, Samuel

Abstract

Asymptotic distributional theorems are presented for the maximal sojourn duration on a semi-Markov chain and for the first passage time until a lengthy duration. Our analysis characterizes the limiting behavior of the longest "generalized success outcome" on a semi-Markov chain. The models include long runs on a single state, on a group of states, and on a set of transitions between states. Applications to success durations containing interruptions and to durations having infinite mean length are also presented.

Suggested Citation

  • Fousler, David E. & Karlin, Samuel, 1987. "Maximal success durations for a semi-Markov process," Stochastic Processes and their Applications, Elsevier, vol. 24(2), pages 203-224, May.
    • Handle: RePEc:eee:spapps:v:24:y:1987:i:2:p:203-224
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    Cited by:

    1. Ourania Chryssaphinou & Stavros Papastavridis & Eutichia Vaggelatou, 1999. "On the Number of Appearances of a Word in a Sequence of I.I.D. Trials," Methodology and Computing in Applied Probability, Springer, vol. 1(3), pages 329-348, October.

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