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Limiting Distributions of a Non-Homogeneous Markov System in a Stochastic Environment in Continuous Time

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  • P. -C. G. Vassiliou

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

Abstract

The stochastic process non-homogeneous Markov system in a stochastic environment in continuous time (S-NHMSC) is introduced in the present paper. The ordinary non-homogeneous Markov process is a very special case of an S-NHMSC. I studied the expected population structure of the S-NHMSC, the first central classical problem of finding the conditions under which the asymptotic behavior of the expected population structure exists and the second central problem of finding which expected relative population structures are possible limiting ones, provided that the limiting vector of input probabilities into the population is controlled. Finally, the rate of convergence was studied.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:8:p:1214-:d:789063
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    References listed on IDEAS

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    1. Zeifman, A. I. & Isaacson, Dean L., 1994. "On strong ergodicity for nonhomogeneous continuous-time Markov chains," Stochastic Processes and their Applications, Elsevier, vol. 50(2), pages 263-273, April.
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    4. 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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    6. Zeifman, A.I. & Korolev, V.Yu. & Satin, Ya.A. & Kiseleva, K.M., 2018. "Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 84-90.
    7. 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.
    8. N. Tsantas, 2001. "Ergodic behavior of a Markov chain model in a stochastic environment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 54(1), pages 101-117, October.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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