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

This article is cited in 63 scientific papers (total in 63 papers)

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).

Full text: PDF file (2375 kB)

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

Received: 30.06.1961

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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    Citing articles on Google Scholar: Russian citations, English citations
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