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

Mathematics

Irina Gudkova¹  Elena Fokicheva²  Tatyana Panfilova²  Anna Sinitcina²  Yacov Satin²  Anastasia Kryukova²  Galina Shilova²  Alexander Sipin²  Ksenia Kiseleva²  Alexander Zeifman³ 

[1] 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;Faculty of Applied Mathematics, Computer Technologies and Physics, Vologda State University, 160000 Vologda, Russia;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;

关键词: continuous-time Markov chains;    catastrophes;    bounds;    birth-death process;    rate of convergence;   

DOI  :  10.3390/math6050080

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown