IDEAS home Printed from https://ideas.repec.org/a/wly/apsmda/v13y1997i3-4p159-176.html
   My bibliography  Save this article

The evolution of the theory of non‐homogeneous Markov systems

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/(SICI)1099-0747(199709/12)13:3/43.0.CO;2-Q
    Download Restriction: no
    File URL: https://libkey.io/10.1002/(SICI)1099-0747(199709/12)13:3/43.0.CO;2-Q?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. P.-C.G. Vassiliou, 2021. "Non-Homogeneous Markov Set Systems," Mathematics, MDPI, vol. 9(5), pages 1-25, February.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:apsmda:v:13:y:1997:i:3-4:p:159-176. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1099-0747 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.