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.

Authors
Zeifman A.I.1, 2, 3 , Korolev V.Y.2, 4, 5 , Satin Y.A.1 , Kiseleva K.M. 1
Journal
Statistics and Probability Letters
Publisher
Elsevier B.V.
Language
English
Pages
84-90
Status
Published
Link
External link
DOI
10.1016/j.spl.2018.01.001
Volume
137
Year
2018
Organizations
  • 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
Keywords
Continuous-time Markov chains; Ergodicity bounds; Inhomogeneous Markov chains; Special norms
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6641/
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