Lower bounds for the rate of convergence for continuous-time inhomogeneous Markov chains with a finite state space

An approach is proposed to the construction of general lower bounds for the rate of convergence of probability characteristics of continuous-time inhomogeneous Markov chains with a finite state space in terms of special “weighted” norms related to total variation. We study the sharpness of these bounds for finite birth–death–catastrophes process and for a Markov chain with large output intensity from a state. © 2018 Elsevier B.V.

Авторы
Zeifman A.I. 1, 2, 3 , Korolev V.Y. 2, 4, 5 , Satin Y.A. 1 , Kiseleva K.M. 1
Журнал
Statistics and Probability Letters
Издательство
Elsevier B.V.
Язык
Английский
Страницы
84-90
Статус
Опубликовано
Ссылка
Внешняя ссылка
DOI
10.1016/J.SPL.2018.01.001
Том
137
Год
2018
Организации
  • 1 Vologda State University, Russian Federation
  • 2 Institute of Informatics Problems, Federal Research Center “Informatics and Control”, Russian Academy of Sciences, Russian Federation
  • 3 Vologda Research Center, Russian Academy of Sciences, Russian Federation
  • 4 Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russian Federation
  • 5 Hangzhou Dianzi University, China
  • 6 Peoples Friendship University of Russia (RUDN University), Vologda State University, Russian Federation
Ключевые слова
Continuous-time Markov chains; Ergodicity bounds; Inhomogeneous Markov chains; Special norms
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