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On obtaining sharp bounds of the rate of convergence for a class of continuous-time Markov chains

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  • Zeifman, A.I.
  • Satin, Y.A.
  • Kiseleva, K.M.

Abstract

We study inhomogeneous continuous-time weakly ergodic Markov chains with a finite state space. We introduce the notion of a Markov chain with the regular structure of an infinitesimal matrix and study the sharp upper bounds on the rate of convergence for such class of Markov chains.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:161:y:2020:i:c:s016771522030033x
    DOI: 10.1016/j.spl.2020.108730
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    References listed on IDEAS

    as
    1. Zeifman, A. & Satin, Y. & Kiseleva, K. & Korolev, V. & Panfilova, T., 2019. "On limiting characteristics for a non-stationary two-processor heterogeneous system," Applied Mathematics and Computation, Elsevier, vol. 351(C), pages 48-65.
    2. 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.
    3. 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.
    4. 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.
    5. Boris L. Granovsky & A. I. Zeifman, 2000. "The N‐limit of spectral gap of a class of birth–death Markov chains," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 16(4), pages 235-248, October.
    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. Di Crescenzo, Antonio & Giorno, Virginia & Nobile, Amelia G., 2016. "Constructing transient birth–death processes by means of suitable transformations," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 152-171.
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