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,
Elena Fokicheva
Affiliations
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
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.
