Maximal success durations for a semi-Markov process

David E. Fousler and Samuel Karlin

Stochastic Processes and their Applications, 1987, vol. 24, issue 2, 203-224

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.

Keywords: success; duration; semi-Markov; process; first; passage; time; exponential; limit; distribution (search for similar items in EconPapers)
Date: 1987
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