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Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities

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  • Aleka Papadopoulou

    (Aristotle University of Thessaloniki)

  • George Tsaklidis

    (Aristotle University of Thessaloniki)

Abstract

In the present paper, the reward paths in non homogeneous semi-Markov systems in discrete time are examined with stochastic selection of the transition probabilities. The mean entrance probabilities and the mean rewards in the course of time are evaluated. Then the rate of the total reward for the homogeneous case is examined and the mean total reward is evaluated by means of p.g.f’s.

Suggested Citation

  • Aleka Papadopoulou & George Tsaklidis, 2007. "Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 399-411, September.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:3:d:10.1007_s11009-007-9027-5
    DOI: 10.1007/s11009-007-9027-5
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    References listed on IDEAS

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    1. Janssen, J. & de Dominicis, R., 1984. "Finite non-homogeneous semi-Markov processes: Theoretical and computational aspects," Insurance: Mathematics and Economics, Elsevier, vol. 3(3), pages 157-165, July.
    2. L. Jianyong & Z. Xiaobo, 2004. "On Average Reward Semi-Markov Decision Processes with a General Multichain Structure," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 339-352, May.
    3. TEUGELS, Jozef L., 1976. "A bibliography on semi-Markov processes," LIDAM Reprints CORE 252, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Erhan Çinlar, 1975. "Exceptional Paper--Markov Renewal Theory: A Survey," Management Science, INFORMS, vol. 21(7), pages 727-752, March.
    5. A. A. Papadopoulou, 1997. "Counting transitions—entrance probabilities in non‐homogeneous semi‐Markov systems," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 199-206, September.
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    Cited by:

    1. Guglielmo D’Amico & Filippo Petroni & Flavio Prattico, 2015. "Performance Analysis of Second Order Semi-Markov Chains: An Application to Wind Energy Production," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 781-794, September.
    2. Zacharias Kyritsis & Aleka Papadopoulou, 2017. "The Quality of Life Via Semi Markov Reward Modelling," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1029-1045, December.
    3. Tim De Feyter & Marie-Anne Guerry & Komarudin, 2017. "Optimizing cost-effectiveness in a stochastic Markov manpower planning system under control by recruitment," Annals of Operations Research, Springer, vol. 253(1), pages 117-131, June.
    4. Aleka A. Papadopoulou & George Tsaklidis & Sally McClean & Lalit Garg, 2012. "On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 717-737, September.
    5. Guglielmo D'Amico & Ada Lika & Filippo Petroni, 2019. "Risk Management of Pension Fund: A Model for Salary Evolution," IJFS, MDPI, vol. 7(3), pages 1-17, August.

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