On the bounds for a two-dimensional birth-death process with catastrophes

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. © 2018 by the authors.

Авторы
Sinitcina A.1 , Satin Y.1 , Zeifman A.2 , Shilova G.1 , Sipin A.1 , Kiseleva K. 1 , Panfilova T.1 , Kryukova A.1 , Gudkova I. 3 , Fokicheva E.1
Журнал
Mathematics
Издательство
MDPI AG
Номер выпуска
5
Язык
Английский
Статус
Опубликовано
Ссылка
Внешняя ссылка
DOI
10.3390/MATH6050080
Номер
80
Том
6
Год
2018
Организации
  • 1 Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, Vologda, 160000, Russian Federation
  • 2 Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, Vologda Research Center of the Russian Academy of SciencesSciences, Ins. of Informatics Problems, Federal Research Center 'Computer Science and Control' of the Russian Academy of Sciences, Vologda, 160000, Russian Federation
  • 3 Applied Probability and Informatics Dep., Peoples' Friendship University of Russia (RUDN Univ.), Institute of Informatics Problems, Federal Research Center 'Computer Science and Control' of the Russian Academy of Sciences, Moskva, 117198, Russian Federation
Ключевые слова
Birth-death process; Bounds; Catastrophes; Continuous-time Markov chains; Rate of convergence
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