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On the Bounds for a Two-Dimensional Birth-Death Process with Catastrophes

Author

Listed:
  • Anna Sinitcina

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Yacov Satin

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Alexander Zeifman

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Vologda Research Center of the Russian Academy of SciencesSciences, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Galina Shilova

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Alexander Sipin

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Ksenia Kiseleva

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Tatyana Panfilova

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Anastasia Kryukova

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

  • Irina Gudkova

    (Applied Probability and Informatics Department, Peoples’ Friendship University of Russia (RUDN University), Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 117198 Moskva, Russia
    These authors contributed equally to this work.)

  • Elena Fokicheva

    (Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
    These authors contributed equally to this work.)

Abstract

The model of a two-dimensional birth-death process with possible catastrophes is studied. The upper bounds on the rate of convergence in some weighted norms and the corresponding perturbation bounds are obtained. In addition, we consider the detailed description of two examples with 1-periodic intensities and various types of death (service) rates. The bounds on the rate of convergence and the behavior of the corresponding mathematical expectations are obtained for each example.

Suggested Citation

  • Anna Sinitcina & Yacov Satin & Alexander Zeifman & Galina Shilova & Alexander Sipin & Ksenia Kiseleva & Tatyana Panfilova & Anastasia Kryukova & Irina Gudkova & Elena Fokicheva, 2018. "On the Bounds for a Two-Dimensional Birth-Death Process with Catastrophes," Mathematics, MDPI, vol. 6(5), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:5:p:80-:d:145813
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    References listed on IDEAS

    as
    1. Antonio Crescenzo & Virginia Giorno & Balasubramanian Krishna Kumar & Amelia G. Nobile, 2012. "A Double-ended Queue with Catastrophes and Repairs, and a Jump-diffusion Approximation," Methodology and Computing in Applied Probability, Springer, vol. 14(4), pages 937-954, December.
    2. Di Crescenzo, A. & Giorno, V. & Nobile, A.G. & Ricciardi, L.M., 2008. "A note on birth-death processes with catastrophes," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2248-2257, October.
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