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Ergodicity Bounds and Limiting Characteristics for a Modified Prendiville Model

Author

Listed:
  • Ilya Usov

    (Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia)

  • Yacov Satin

    (Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia)

  • Alexander Zeifman

    (Department of Applied Mathematics, Vologda State University, 15 Lenina Str., 160000 Vologda, Russia
    Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova Str., 119333 Moscow, Russia
    Vologda Research Center of the Russian Academy of Sciences, 556A Gorky Str., 160014 Vologda, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia)

  • Victor Korolev

    (Federal Research Center “Computer Sciences and Control” of the Russian Academy of Sciences, 44-2 Vavilova Str., 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia
    Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory, 119899 Moscow, Russia)

Abstract

We consider the time-inhomogeneous Prendiville model with failures and repairs. The property of weak ergodicity is considered, and estimates of the rate of convergence for the main probabilistic characteristics of the model are obtained. Several examples are considered showing how such estimates are obtained and how the limiting characteristics themselves are constructed.

Suggested Citation

  • Ilya Usov & Yacov Satin & Alexander Zeifman & Victor Korolev, 2022. "Ergodicity Bounds and Limiting Characteristics for a Modified Prendiville Model," Mathematics, MDPI, vol. 10(23), pages 1-14, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4401-:d:980387
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    References listed on IDEAS

    as
    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. Virginia Giorno & Amelia G. Nobile, 2020. "Bell Polynomial Approach for Time-Inhomogeneous Linear Birth–Death Process with Immigration," Mathematics, MDPI, vol. 8(7), pages 1-29, July.
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