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On strong ergodicity for nonhomogeneous continuous-time Markov chains

Author

Listed:
  • Zeifman, A. I.
  • Isaacson, Dean L.

Abstract

Let X(t) be a nonhomogeneous continuous-time Markov chain. Suppose that the intensity matrices of X(t) and some weakly or strongly ergodic Markov chain X(t) are close. Some sufficient conditions for weak and strong ergodicity of X(t) are given and estimates of the rate of convergence are proved. Queue-length for a birth and death process in the case of asymptotically proportional intensities is considered as an example.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:50:y:1994:i:2:p:263-273
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    Citations

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    Cited by:

    1. Alexander Zeifman & Victor Korolev & Yacov Satin, 2020. "Two Approaches to the Construction of Perturbation Bounds for Continuous-Time Markov Chains," Mathematics, MDPI, vol. 8(2), pages 1-25, February.
    2. Giorno, Virginia & Nobile, Amelia G., 2020. "On a class of birth-death processes with time-varying intensity functions," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    3. Alexander Y. Mitrophanov, 2024. "The Arsenal of Perturbation Bounds for Finite Continuous-Time Markov Chains: A Perspective," Mathematics, MDPI, vol. 12(11), pages 1-15, May.
    4. 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.
    5. Zeifman, A.I. & Korolev, V.Yu., 2014. "On perturbation bounds for continuous-time Markov chains," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 66-72.
    6. Yacov Satin & Alexander Zeifman & Alexander Sipin & Sherif I. Ammar & Janos Sztrik, 2020. "On Probability Characteristics for a Class of Queueing Models with Impatient Customers," Mathematics, MDPI, vol. 8(4), pages 1-15, April.

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