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The evolution of the theory of non‐homogeneous Markov systems

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  • P.‐C. G. Vassiliou

Abstract

A review of the evolution of the theory of non‐homogeneous Markov systems (NHMSs) is given. It starts with the definition of the stochastic process NHMS, discusses the variability of the process and provides as examples some real applications of the theory. Then, important novel ideas and basic theorems are presented on: (i) the asymptotic behaviour of NHMSs; (ii) control theory; (iii) cyclic behaviour; (iv) physics of populations: stability, entropy, energy; (v) non‐homogeneous semi‐Markov systems; (vi) the NHMS in a stochastic environment. © 1998 John Wiley & Sons, Ltd.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:apsmda:v:13:y:1997:i:3-4:p:159-176
    DOI: 10.1002/(SICI)1099-0747(199709/12)13:3/43.0.CO;2-Q
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    Cited by:

    1. P.-C. G. Vassiliou, 2020. "Laws of Large Numbers for Non-Homogeneous Markov Systems," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1631-1658, December.
    2. P. -C. G. Vassiliou, 2020. "Rate of Convergence and Periodicity of the Expected Population Structure of Markov Systems that Live in a General State Space," Mathematics, MDPI, vol. 8(6), pages 1-23, 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.
    4. 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.
    5. P.-C.G. Vassiliou & Andreas C. Georgiou, 2021. "Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields," Mathematics, MDPI, vol. 9(19), pages 1-6, October.
    6. 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.
    7. Andreas C. Georgiou & Alexandra Papadopoulou & Pavlos Kolias & Haris Palikrousis & Evanthia Farmakioti, 2021. "On State Occupancies, First Passage Times and Duration in Non-Homogeneous Semi-Markov Chains," Mathematics, MDPI, vol. 9(15), pages 1-17, July.
    8. P.-C. G. Vassiliou & T. P. Moysiadis, 2010. "$\boldsymbol{\mathcal{G}-}$ Inhomogeneous Markov Systems of High Order," Methodology and Computing in Applied Probability, Springer, vol. 12(2), pages 271-292, June.
    9. 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.
    10. P.-C.G. Vassiliou, 2021. "Non-Homogeneous Markov Set Systems," Mathematics, MDPI, vol. 9(5), pages 1-25, February.

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