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On the Distributions of the State Sizes of Closed Continuous Time Homogeneous Markov Systems

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  • G. Vasiliadis

    (Aristotle University of Thessaloniki)

  • G. Tsaklidis

    (Aristotle University of Thessaloniki)

Abstract

The evolution of the state sizes of a closed continuous-time homogeneous Markov system is determined by the convolution of multinomial distributions expressing the number of transitions between the states of the system. In order to investigate the distributions of the state sizes, we provide the computation of their moments, at any time point, via a recursive formula concerning the derivative of the moments. The basic result is given by means of a new vector product which is similar to the Kronecker product. Finally, a formula for the computation of the state sizes distributions is given.

Suggested Citation

  • G. Vasiliadis & G. Tsaklidis, 2009. "On the Distributions of the State Sizes of Closed Continuous Time Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 11(4), pages 561-582, December.
    • Handle: RePEc:spr:metcap:v:11:y:2009:i:4:d:10.1007_s11009-008-9074-6
    DOI: 10.1007/s11009-008-9074-6
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. P. -C. G. Vassiliou, 2022. "Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time," Mathematics, MDPI, vol. 10(8), pages 1-16, April.
    2. Rodi Lykou & George Tsaklidis, 2021. "Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation," Mathematics, MDPI, vol. 9(12), pages 1-16, June.
    3. George Vasiliadis, 2012. "On the Distributions of the State Sizes of the Continuous Time Homogeneous Markov System with Finite State Capacities," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 863-882, September.

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