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$\boldsymbol{\mathcal{G}-}$ Inhomogeneous Markov Systems of High Order

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  • P.-C. G. Vassiliou

    (University College London
    Aristotle University of Thessaloniki)

  • T. P. Moysiadis

    (Aristotle University of Thessaloniki)

Abstract

In the present, we introduce and study the $\mathcal{G-}$ inhomogeneous Markov system of high order, which is a more general in many respects stochastic process than the known inhomogeneous Markov system. We define the inhomogeneous superficial razor cut mixture transition distribution model extending for the homogeneous case the idea of the mixture transition model. With the introduction of the appropriate vector stochastic process and the establishment of relationships among them, we study the asymptotic behaviour of the $\mathcal{G-}$ inhomogeneous Markov system of high order. In the form of two theorems, the asymptotic behaviour of the inherent $\mathcal{G-}$ inhomogeneous Markov chain and the expected and relative expected population structure of the $\mathcal{G-}$ inhomogeneous Markov system of high order, are provided under assumptions easily met in practice. Finally, we provide an illustration of the present results in a manpower system.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:metcap:v:12:y:2010:i:2:d:10.1007_s11009-009-9143-5
    DOI: 10.1007/s11009-009-9143-5
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    References listed on IDEAS

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    1. S. I. McClean & J. O. Gribbin, 1987. "Estimation for incomplete manpower data," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 3(1), pages 13-25.
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    3. F.I. Ugwuowo & S.I. McClean, 2000. "Modelling heterogeneity in a manpower system: a review," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 16(2), pages 99-110, April.
    4. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    5. Adrian Raftery & Simon Tavaré, 1994. "Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 179-199, March.
    6. 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:

    1. Sally McClean & Lingkai Yang, 2023. "Semi-Markov Models for Process Mining in Smart Homes," Mathematics, MDPI, vol. 11(24), pages 1-16, December.

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