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

Anna Sinitcina, Yacov Satin, Alexander Zeifman, Galina Shilova, Alexander Sipin, Ksenia Kiseleva, Tatyana Panfilova, Anastasia Kryukova, Irina Gudkova and Elena Fokicheva
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Anna Sinitcina: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
Yacov Satin: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
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
Galina Shilova: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
Alexander Sipin: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
Ksenia Kiseleva: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
Tatyana Panfilova: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
Anastasia Kryukova: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia
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
Elena Fokicheva: Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia

Mathematics, 2018, vol. 6, issue 5, 1-17

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.

Keywords: continuous-time Markov chains; catastrophes; bounds; birth-death process; rate of convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2018
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