On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains Full article
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Theory of Probability and its Applications
ISSN: 0040-585X , E-ISSN: 1095-7219 |
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| Output data | Year: 2023, Volume: 68, Number: 3, Pages: 456-482 Pages count : 27 DOI: 10.1137/S0040585X97T991519 | ||
| Tags | change-point problem, change-point detection, delay time, number of “false alarms”, Poisson approximation, Markov chain with a positive atom, exponential convergence rate, asymptotically optimal solution | ||
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0010 |
Abstract:
Under the assumption that the change-point time is large, a Poisson approximation for the distribution of the number of false alarms is obtained. We also find upper bounds for the probability of a "false alarm” on a given time interval. An asymptotic expansion for the mean delay time of the alarm signal relative to the change-point time is obtained. To get this result, we establish the exponential convergence rate in the ergodic theorem for Markov chains with a positive atom; chains of this kind describe the monitoring of control systems. A game-theoretic approach is employed to obtain asymptotically optimal solutions of the change-point problem.
Cite:
Borovkov A.A.
On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains
Theory of Probability and its Applications. 2023. V.68. N3. P.456-482. DOI: 10.1137/S0040585X97T991519 WOS Scopus РИНЦ OpenAlex
On the Asymptotic Approach to the Change-Point Problem and Exponential Convergence Rate in the Ergodic Theorem for Markov Chains
Theory of Probability and its Applications. 2023. V.68. N3. P.456-482. DOI: 10.1137/S0040585X97T991519 WOS Scopus РИНЦ OpenAlex
Original:
Borovkov A.A.
Об асимптотическом подходе к задаче о разладке и экспоненциальной сходимости в эргодической теореме для цепей Маркова
Теория вероятностей и ее применения. 2023. Т.68. №3. С.456-482. DOI: 10.4213/tvp5642 РИНЦ OpenAlex
Об асимптотическом подходе к задаче о разладке и экспоненциальной сходимости в эргодической теореме для цепей Маркова
Теория вероятностей и ее применения. 2023. Т.68. №3. С.456-482. DOI: 10.4213/tvp5642 РИНЦ OpenAlex
Dates:
| Published print: | Nov 30, 2023 |
| Published online: | Nov 30, 2023 |
Identifiers:
| Web of science: | WOS:001108619900012 |
| Scopus: | 2-s2.0-85179371498 |
| Elibrary: | 64001722 |
| OpenAlex: | W4388464845 |