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Mathematics 2018, 6(5), 80; https://doi.org/10.3390/math6050080

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

1
Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
2
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
3
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
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Received: 19 April 2018 / Revised: 8 May 2018 / Accepted: 8 May 2018 / Published: 11 May 2018
(This article belongs to the Special Issue Stochastic Processes with Applications)
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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. View Full-Text
Keywords: continuous-time Markov chains; catastrophes; bounds; birth-death process; rate of convergence continuous-time Markov chains; catastrophes; bounds; birth-death process; rate of convergence
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Sinitcina, A.; Satin, Y.; Zeifman, A.; Shilova, G.; Sipin, A.; Kiseleva, K.; Panfilova, T.; Kryukova, A.; Gudkova, I.; Fokicheva, E. On the Bounds for a Two-Dimensional Birth-Death Process with Catastrophes. Mathematics 2018, 6, 80.

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