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 Teor. Veroyatnost. i Primenen., 1963, Volume 8, Issue 1, Pages 26–51 (Mi tvp4645)

On Optimum Methods in Quickest Detection Problems

A. N. Shiryaev

Moscow

Abstract: In this paper optimum methods are developed for observing a process (1), in which the moment when a "disorder" $\theta$ appears is not known. The basic quantity characterizing the quality of this observation method is the mean time delay $\tau$ for detection of a disorder.
After making assumption (4) it is shown that for a set false alarm probability $\omega$ or for a set $\mathbf{N}$ – mathematical expectation of false alarm numbers occurring up till the moment the disorder appears the observation method minimizing $\tau=\tau(\omega)$ or $\tau=\tau(\mathbf{N})$ is based on an observation of aposteriori probability (23).
In § 3 a case is considered, wherein the disorder appears on the background of steadystate conditions arising when the disordes is absent. A method is found for minimizing $\tau=\tau(\mathbf{T})$ for a set $\mathbf{T}$ – mathematical expectation of the time between two false alarms. The dependency $\tau=\tau(\mathbf{T})$ is given by formula (36).

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English version:
Theory of Probability and its Applications, 1963, 8:1, 22–46

Citation: A. N. Shiryaev, “On Optimum Methods in Quickest Detection Problems”, Teor. Veroyatnost. i Primenen., 8:1 (1963), 26–51; Theory Probab. Appl., 8:1 (1963), 22–46

Citation in format AMSBIB
\Bibitem{Shi63} \by A.~N.~Shiryaev \paper On Optimum Methods in Quickest Detection Problems \jour Teor. Veroyatnost. i Primenen. \yr 1963 \vol 8 \issue 1 \pages 26--51 \mathnet{http://mi.mathnet.ru/tvp4645} \transl \jour Theory Probab. Appl. \yr 1963 \vol 8 \issue 1 \pages 22--46 \crossref{https://doi.org/10.1137/1108002} 

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