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On the Distributions of the State Sizes of Discrete Time Homogeneous Markov Systems

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  • G. Vasiliadis

    (Aristotle University of Thessaloniki)

  • G. Tsaklidis

    (Aristotle University of Thessaloniki)

Abstract

The evolution of a closed discrete-time homogeneous Markov system (HMS) is determined by the evolution of its state sizes in time. In order to examine the variability of the state sizes, their moments are evaluated for any time point, and recursive formulae for their computation are derived. As a consequence the asymptotic values of the moments for a convergent HMS can be evaluated. The respective recursive formula for a HMS with periodic transition matrix is given. The p.d.f.’s of the state sizes follow directly by means of the moments. The theoretical results are illustrated by a numerical example.

Suggested Citation

  • G. Vasiliadis & G. Tsaklidis, 2008. "On the Distributions of the State Sizes of Discrete Time Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 10(1), pages 55-71, March.
    • Handle: RePEc:spr:metcap:v:10:y:2008:i:1:d:10.1007_s11009-007-9034-6
    DOI: 10.1007/s11009-007-9034-6
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    References listed on IDEAS

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    1. G. J. Taylor & S. I. McClean & P. H. Millard, 2000. "Stochastic models of geriatric patient bed occupancy behaviour," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 163(1), pages 39-48.
    2. P.‐C. G. Vassiliou, 1997. "The evolution of the theory of non‐homogeneous Markov systems," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 159-176, September.
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    Cited by:

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    2. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.

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