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A Continuous-Time Semi-Markov System Governed by Stepwise Transitions

Author

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  • Vlad Stefan Barbu

    (Laboratory of Mathematics Raphaël Salem, University of Rouen-Normandy, UMR 6085, Avenue de l’Université, BP.12, F-76801 Saint-Étienne-du-Rouvray, France)

  • Guglielmo D’Amico

    (Department of Economics, University “G. d’Annunzio” of Chieti-Pescara, Viale Pindaro 42, 65127 Pescara, Italy)

  • Andreas Makrides

    (Department of Statistics and Actuarial-Financial Mathematics, University of the Aegean, GR-83200 Samos, Greece)

Abstract

In this paper, we introduce a class of stochastic processes in continuous time, called step semi-Markov processes. The main idea comes from bringing an additional insight to a classical semi-Markov process: the transition between two states is accomplished through two or several steps. This is an extension of a previous work on discrete-time step semi-Markov processes. After defining the models and the main characteristics of interest, we derive the recursive evolution equations for two-step semi-Markov processes.

Suggested Citation

  • Vlad Stefan Barbu & Guglielmo D’Amico & Andreas Makrides, 2022. "A Continuous-Time Semi-Markov System Governed by Stepwise Transitions," Mathematics, MDPI, vol. 10(15), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2745-:d:879207
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    References listed on IDEAS

    as
    1. Moura, Márcio das Chagas & Droguett, Enrique López, 2009. "Mathematical formulation and numerical treatment based on transition frequency densities and quadrature methods for non-homogeneous semi-Markov processes," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 342-349.
    2. Gianfranco Corradi & Jacques Janssen & Raimondo Manca, 2004. "Numerical Treatment of Homogeneous Semi-Markov Processes in Transient Case–a Straightforward Approach," Methodology and Computing in Applied Probability, Springer, vol. 6(2), pages 233-246, June.
    3. I. Votsi & G. Gayraud & V. S. Barbu & N. Limnios, 2021. "Hypotheses testing and posterior concentration rates for semi-Markov processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(3), pages 707-732, October.
    4. Ernst, A. T. & Jiang, H. & Krishnamoorthy, M. & Sier, D., 2004. "Staff scheduling and rostering: A review of applications, methods and models," European Journal of Operational Research, Elsevier, vol. 153(1), pages 3-27, February.
    5. Vlad Stefan Barbu & Slim Beltaief & Serguei Pergamenchtchikov, 2022. "Adaptive efficient estimation for generalized semi-Markov big data models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(5), pages 925-955, October.
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