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ROCOF of higher order for semi-Markov processes

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  • D’Amico, Guglielmo
  • Petroni, Filippo

Abstract

In this paper, we study the rate of occurrence of failures (ROCOF) of higher order for continuous time semi-Markov processes (SMP). This indicator gives information on whether there are a lot of failures or only a few within a time interval. It also considers the relative positioning of tuples of failures in time. Here, we consider SMP with a mixed probability distribution for the initial law of the system taking into account the possible random starting from any state with any duration. Furthermore, under suitable assumptions on the transition rates, we determine an explicit formula for the ROCOF of higher order and we recover as particular cases previous results obtained in the literature. A numerical example demonstrates the possibility of using this index in real applications. A possible application in the field of mathematical finance is also discussed.

Suggested Citation

  • D’Amico, Guglielmo & Petroni, Filippo, 2023. "ROCOF of higher order for semi-Markov processes," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007871
    DOI: 10.1016/j.amc.2022.127719
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    References listed on IDEAS

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    13. Irene Votsi & Nikolaos Limnios & George Tsaklidis & Eleftheria Papadimitriou, 2012. "Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 685-703, September.
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