Geodesic
On an asymptotic approach to the change point detection problem and exponential
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 456-482

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: 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. 
@article{TVP_2023_68_3_a2,
     author = {A. A. Borovkov},
     title = {On an asymptotic approach to the change point detection problem and exponential},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {456--482},
     publisher = {mathdoc},
     volume = {68},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a2/}
}
TY  - JOUR
AU  - A. A. Borovkov
TI  - On an asymptotic approach to the change point detection problem and exponential
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2023
SP  - 456
EP  - 482
VL  - 68
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a2/
LA  - ru
ID  - TVP_2023_68_3_a2
ER  - 
%0 Journal Article
%A A. A. Borovkov
%T On an asymptotic approach to the change point detection problem and exponential
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2023
%P 456-482
%V 68
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a2/
%G ru
%F TVP_2023_68_3_a2
A. A. Borovkov. On an asymptotic approach to the change point detection problem and exponential. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 3, pp. 456-482. http://geodesic.mathdoc.fr/item/TVP_2023_68_3_a2/