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The first-passage times of phase semi-Markov processes

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  • Zhang, Xuan
  • Hou, Zhenting

Abstract

In this paper, we consider a class of semi-Markov processes, known as phase semi-Markov processes, which can be considered as an extension of Markov processes, but whose times between transitions are phase-type random variables. Based on the theory of generalized inverses, we derive expressions for the moments of the first-passage time distributions, generalizing the results obtained by Kemeny and Snell (1960) for Markov chains.

Suggested Citation

  • Zhang, Xuan & Hou, Zhenting, 2012. "The first-passage times of phase semi-Markov processes," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 40-48.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:1:p:40-48
    DOI: 10.1016/j.spl.2011.08.021
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    References listed on IDEAS

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    1. Mark Fackrell, 2009. "Modelling healthcare systems with phase-type distributions," Health Care Management Science, Springer, vol. 12(1), pages 11-26, March.
    2. Fygenson, Mendel, 1989. "A fundamental matrix for regular semi-Markov processes," Stochastic Processes and their Applications, Elsevier, vol. 32(1), pages 151-160, June.
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    Cited by:

    1. Richard L. Warr, 2014. "Numerical Approximation of Probability Mass Functions via the Inverse Discrete Fourier Transform," Methodology and Computing in Applied Probability, Springer, vol. 16(4), pages 1025-1038, December.
    2. Grossmann, Wolf D. & Grossmann, Iris & Steininger, Karl W., 2014. "Solar electricity generation across large geographic areas, Part II: A Pan-American energy system based on solar," Renewable and Sustainable Energy Reviews, Elsevier, vol. 32(C), pages 983-993.
    3. Andreas C. Georgiou & Alexandra Papadopoulou & Pavlos Kolias & Haris Palikrousis & Evanthia Farmakioti, 2021. "On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    4. Guoxin Su & Li Liu, 2024. "Workflow Trace Profiling and Execution Time Analysis in Quantitative Verification," Future Internet, MDPI, vol. 16(9), pages 1-19, September.

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