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A Unified Approach for Hitting Time of Jump Markov Type Processes

Author

Listed:
  • Nikolaos Limnios

    (Université de Technologie de Compiègne, Sorbonne University Alliance)

  • Bei Wu

    (Northwestern Polytechnical University)

Abstract

This paper investigates the asymptotic analysis of the hitting time of Markov-type jump processes (i.e., semi-Markov, Markov, in continuous or discrete time) with a small probability of entering a non-empty terminal subset. This means that absorption is a rare event. The mean hitting time function of all four type processes obeyed the same equation. We obtain unified results of asymptotic approximation in a series scheme or, equivalently, a functional type of mean hitting time.

Suggested Citation

  • Nikolaos Limnios & Bei Wu, 2024. "A Unified Approach for Hitting Time of Jump Markov Type Processes," Methodology and Computing in Applied Probability, Springer, vol. 26(3), pages 1-10, September.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:3:d:10.1007_s11009-024-10100-2
    DOI: 10.1007/s11009-024-10100-2
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    References listed on IDEAS

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    1. Nikolaos Limnios, 2012. "Reliability Measures of Semi-Markov Systems with General State Space," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 895-917, December.
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