Informatics and Applications
2025, Volume 19, Issue 1, pp 67-73
PERTURBATION AND TRUNCATION BOUNDS FOR ONE CLASS OF MARKOV PROCESSES OF BIRTH-AND-DEATH TYPE WITH CATASTROPHES
- I. A. Usov
- Y. A. Satin
- A. I. Zeifman
- V. Yu. Korolev
Abstract
A class of inhomogeneous continuous-time Markov chains of birth-and-death type with a countable state space is considered. Two types of additional transitions are allowed in the chain, which bring it either to the boundary state or to the state adjacent to it. It is assumed that with an increase in the state number, the birth (death) intensities monotonically decrease (increase). Perturbation bounds are obtained using special weighted norms associated with the total variation. An estimate of the approximation error, when one replaces the original chain by a process with a finite number of states, is constructed. For the case when all the intensities are state-dependent, conditions are provided (using the logarithmic norm method), which guarantee (weak) ergodicity in the norm of total variation. Results are accompanied by illustrative examples.
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[+] About this article
Title
PERTURBATION AND TRUNCATION BOUNDS FOR ONE CLASS OF MARKOV PROCESSES OF BIRTH-AND-DEATH TYPE WITH CATASTROPHES
Journal
Informatics and Applications
2025, Volume 19, Issue 1, pp 67-73
Cover Date
2025-04-01
DOI
10.14357/19922264250109
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing system; birth-and-death process; catastrophes; truncation bounds; perturbation bounds
Authors
I. A. Usov  , Y. A. Satin  ,  , A. I. Zeifman  ,  , and V. Yu. Korolev  ,  ,
Author Affiliations
 Department of Applied Mathematics, Vologda State University, 15 Lenin Str., Vologda 160000, Russian Federation
 Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
 Moscow Center for Fundamental and Applied Mathematics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
 Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskie Gory, GSP-1, Moscow 119991, Russian Federation
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