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Two-sided bounds on the rate of convergence for continuous-time finite inhomogeneous Markov chains

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  • Zeifman, A.I.
  • Korolev, V. Yu.

Abstract

We suggest an approach to obtain general two-sided bounds on the rate of convergence in terms of special “weighted” norms related to total variation. Some important classes of continuous-time Markov chains are considered: birth–death–catastrophes processes, queueing models with batch arrivals and group services, chains with absorption in zero.

Suggested Citation

  • Zeifman, A.I. & Korolev, V. Yu., 2015. "Two-sided bounds on the rate of convergence for continuous-time finite inhomogeneous Markov chains," Statistics & Probability Letters, Elsevier, vol. 103(C), pages 30-36.
    • Handle: RePEc:eee:stapro:v:103:y:2015:i:c:p:30-36
    DOI: 10.1016/j.spl.2015.04.013
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    References listed on IDEAS

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    1. 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.
    2. Granovsky, Boris L. & Zeifman, Alexander I., 1997. "The decay function of nonhomogeneous birth-death processes, with application to mean-field models," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 105-120, December.
    3. Zeifman, A.I., 1995. "Upper and lower bounds on the rate of convergence for nonhomogeneous birth and death processes," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 157-173, September.
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    Cited by:

    1. 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.
    2. Zeifman, A.I. & Satin, Y.A. & Kiseleva, K.M., 2020. "On obtaining sharp bounds of the rate of convergence for a class of continuous-time Markov chains," Statistics & Probability Letters, Elsevier, vol. 161(C).
    3. 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.

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