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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 3, Pages 610–622 (Mi tvp2456)  

This article is cited in 4 scientific papers (total in 4 papers)

On the Best 2-CUSUM Stopping Rule for Quickest Detection of Two-Sided Alternatives in a Brownian Motion Model

O. Hadjiliadisa, V. H. Poorb

a Columbia University
b Princeton University

Abstract: This work examines the problem of sequential detection of a change in the drift of a Brownian motion in the case of two-sided alternatives. Traditionally, 2-CUSUM stopping rules have been used for this problem due to their asymptotically optimal character as the mean time between false alarms tends to $\infty$. In particular, attention has focused on 2-CUSUM harmonic mean rules due to the simplicity of calculating their first moments. In this paper, expressions for the first moment of a general 2-CUSUM stopping rule and its rate of change are derived. These expressions are used to obtain explicit upper and lower bounds for it and its rate of change as one of the threshold parameters changes. Using these expressions we prove not only the existence but also the uniqueness of the best classical 2-CUSUM stopping rule with respect to the extended Lorden criterion suggested in [O. Hadjiliadis and G. V. Moustakides, Theory Probab. Appl., 50 (2006), pp. 75–85]. In particular, in both the symmetric and the nonsymmetric case we identify the class of the best 2-CUSUM stopping rule

Keywords: change detection, quickest detection, CUSUM, two-sided CUSUM.

DOI: https://doi.org/10.4213/tvp2456

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English version:
Theory of Probability and its Applications, 2009, 53:3, 537–547

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Received: 23.05.2007

Citation: O. Hadjiliadis, V. H. Poor, “On the Best 2-CUSUM Stopping Rule for Quickest Detection of Two-Sided Alternatives in a Brownian Motion Model”, Teor. Veroyatnost. i Primenen., 53:3 (2008), 610–622; Theory Probab. Appl., 53:3 (2009), 537–547

Citation in format AMSBIB
\by O.~Hadjiliadis, V.~H.~Poor
\paper On the Best 2-CUSUM Stopping Rule for Quickest Detection of Two-Sided Alternatives in a Brownian Motion Model
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 3
\pages 610--622
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 3
\pages 537--547

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    This publication is cited in the following articles:
    1. B. S. Darhovsky, “Change-point detection in random sequence under minimal prior information”, Theory Probab. Appl., 58:3 (2014), 488–493  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Komaee A., “Quickest Detection of a Random Pulse in White Gaussian Noise”, IEEE Trans. Autom. Control, 59:6 (2014), 1468–1479  crossref  mathscinet  zmath  isi  elib  scopus
    3. Moustakides G.V., “Multiple Optimality Properties of the Shewhart Test”, Seq. Anal., 33:3 (2014), 318–344  crossref  mathscinet  zmath  isi  scopus
    4. Zhang H., Hadjiliadis O., Schaefer T., Poor H.V., “Quickest Detection in Coupled Systems”, SIAM J. Control Optim., 52:3 (2014), 1567–1596  crossref  mathscinet  zmath  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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