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Comparison of level-crossing times for Markov and semi-Markov processes

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  • Ferreira, Fátima
  • Pacheco, António

Abstract

We derive sufficient conditions for the level-crossing ordering of continuous-time Markov chains (CTMCs) and semi-Markov processes (SMPs). The former ones constitute a relaxation of Kirstein's conditions for stochastic ordering of CTMCs in the usual sense, whereas the latter ones are an extension of conditions established by Di Crescenzo and Ricciardi and Irle for skip-free-to-the-right SMPs.

Suggested Citation

  • Ferreira, Fátima & Pacheco, António, 2007. "Comparison of level-crossing times for Markov and semi-Markov processes," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 151-157, January.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:2:p:151-157
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    References listed on IDEAS

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    1. Di Crescenzo, Antonio & Ricciardi, Luigi M., 1996. "Comparing first-passage times for semi-Markov skip-free processes," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 247-256, October.
    2. David Sonderman, 1980. "Comparing Semi-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 110-119, February.
    3. Ward Whitt, 1986. "Stochastic Comparisons for Non-Markov Processes," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 608-618, November.
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    Cited by:

    1. Emilio De Santis & Fabio Spizzichino, 2016. "Some Sufficient Conditions for Stochastic Comparisons Between Hitting Times for Skip-free Markov Chains," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1021-1034, December.

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