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Some Sufficient Conditions for Stochastic Comparisons Between Hitting Times for Skip-free Markov Chains

Author

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  • Emilio De Santis

    (La Sapienza University)

  • Fabio Spizzichino

    (La Sapienza University)

Abstract

We develop some sufficient conditions for the usual stochastic ordering between hitting times, of a fixed state, for two finite Markov chains with the same state-space. Our attention will be focused on the so called skip-free case and, for the proof of our results, we develop a special type of coupling. We also analyze some special cases of applications in the frame of reliability degradation and of times to occurrence of words under random sampling of letters from a finite alphabet. As will be briefly discussed such fields give rise, in a natural way, to skip-free Markov chains.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-016-9486-7
    DOI: 10.1007/s11009-016-9486-7
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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. 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.
    3. Zhou, Ke, 2013. "Hitting time distribution for skip-free Markov chains: A simple proof," Statistics & Probability Letters, Elsevier, vol. 83(7), pages 1782-1786.
    4. Chen, Robert & Zame, Alan, 1979. "On fair coin-tossing games," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 150-156, March.
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    Cited by:

    1. Xiang, Xuyan & Fu, Haiqin & Zhou, Jieming & Deng, Yingchun & Yang, Xiangqun, 2021. "Taboo rate and hitting time distribution of continuous-time reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 169(C).

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    4. 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.

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