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Non-Homogeneous Markov Set Systems

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  • P.-C.G. Vassiliou

    (Department of Statistical Science, University College London, Gower St, London WC1E 6BT, UK)

Abstract

A more realistic way to describe a model is the use of intervals which contain the required values of the parameters. In practice we estimate the parameters from a set of data and it is natural that they will be in confidence intervals. In the present study, we study Non-Homogeneous Markov Systems (NHMS) processes for which the required basic parameters are in intervals. We call such processes Non-Homogeneous Markov Set Systems (NHMSS). First we study the set of the relative expected population structure of memberships and we prove that under certain conditions of convexity of the intervals of the parameters the set is compact and convex. Next, we establish that if the NHMSS starts with two different initial distributions sets and allocation probability sets under certain conditions, asymptotically the two expected relative population structures coincide geometrically fast. We continue proving a series of theorems on the asymptotic behavior of the expected relative population structure of a NHMSS and the properties of their limit set. Finally, we present an application for geriatric and stroke patients in a hospital and through it we solve problems that surface in an application.

Suggested Citation

  • P.-C.G. Vassiliou, 2021. "Non-Homogeneous Markov Set Systems," Mathematics, MDPI, vol. 9(5), pages 1-25, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:471-:d:505577
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    References listed on IDEAS

    as
    1. Georgiou, A. C. & Vassiliou, P. -C. G., 1997. "Cost models in nonhomogeneous Markov systems," European Journal of Operational Research, Elsevier, vol. 100(1), pages 81-96, July.
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    7. 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.
    8. 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.
    9. S McClean & P Millard, 2007. "Where to treat the older patient? Can Markov models help us better understand the relationship between hospital and community care?," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 255-261, February.
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