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Teor. Veroyatnost. i Primenen., 2005, Volume 50, Issue 1, Pages 131–144 (Mi tvp161)  

This article is cited in 15 scientific papers (total in 15 papers)

Optimal and asymptotically optimal CUSUM rules for change point detection in the Brownian motion model with multiple alternatives

O. Hadjiliadis, V. Moustakides

Columbia University

Abstract: This work examines the problem of sequential change detection in the constant drift of a Brownian motion in the case of multiple alternatives. As a performance measure an extended Lorden's criterion is proposed. When the possible drifts, assumed after the change, have the same sign, the CUSUM rule, designed to detect the smallest in absolute value drift, is proven to be the optimum. If the drifts have opposite signs, then a specific 2-CUSUM rule is shown to be asymptotically optimal as the frequency of false alarms tends to infinity.

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


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English version:
Theory of Probability and its Applications, 2006, 50:1, 75–85

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Received: 16.12.2002

Citation: O. Hadjiliadis, V. Moustakides, “Optimal and asymptotically optimal CUSUM rules for change point detection in the Brownian motion model with multiple alternatives”, Teor. Veroyatnost. i Primenen., 50:1 (2005), 131–144; Theory Probab. Appl., 50:1 (2006), 75–85

Citation in format AMSBIB
\by O.~Hadjiliadis, V.~Moustakides
\paper Optimal and asymptotically optimal CUSUM rules for change point detection in the Brownian motion model with multiple alternatives
\jour Teor. Veroyatnost. i Primenen.
\yr 2005
\vol 50
\issue 1
\pages 131--144
\jour Theory Probab. Appl.
\yr 2006
\vol 50
\issue 1
\pages 75--85

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    This publication is cited in the following articles:
    1. Hadjiliadis O., “Optimality of the 2-CUSUM drift equalizer rules for detecting two-sided alternatives in the Bownian motion model”, J. Appl. Probab., 42:4 (2005), 1183–1193  crossref  mathscinet  zmath  isi  scopus
    2. Hadjiliadis O., Večeř J., “Drawdowns preceding rallies in the Brownian motion model”, Quant. Finance, 6:5 (2006), 403–409  crossref  mathscinet  zmath  isi  scopus
    3. Theory Probab. Appl., 53:3 (2009), 537–547  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Pospisil L., Vecer J., Hadjiliadis O., “Formulas for stopped diffusion processes with stopping times based on drawdowns and drawups”, Stochastic Process. Appl., 119:8 (2009), 2563–2578  crossref  mathscinet  zmath  isi  scopus
    5. Hadjiliadis O., Zhang Hongzhong, Poor H.V., “One shot schemes for decentralized quickest change detection”, IEEE Trans. Inform. Theory, 55:7 (2009), 3346–3359  crossref  mathscinet  zmath  isi  scopus
    6. Dayanik S., “Wiener disorder problem with observations at fixed discrete time epochs”, Math. Oper. Res., 35:4 (2010), 756–785  crossref  mathscinet  zmath  isi  elib  scopus
    7. D'Angelo M. F. S. V., Palhares R.M., Takahashi R.H.C., Loschi R.H., “Fuzzy/Bayesian change point detection approach to incipient fault detection”, Iet Control Theory and Applications, 5:4 (2011), 539–551  crossref  mathscinet  isi  scopus
    8. D'Angelo Marcos F. S. V., Palhares R.M., Takahashi R.H.C., Loschi R.H., Baccarini L.M.R., Caminhas W.M., “Incipient fault detection in induction machine stator-winding using a fuzzy-Bayesian change point detection approach”, Applied Soft Computing, 11:1 (2011), 179–192  crossref  mathscinet  isi  scopus
    9. 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
    10. 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
    11. Moustakides G.V., “Multiple Optimality Properties of the Shewhart Test”, Seq. Anal., 33:3 (2014), 318–344  crossref  mathscinet  zmath  isi  scopus
    12. 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
    13. Molloy T.L., Ford J.J., “Asymptotic Minimax Robust Quickest Change Detection for Dependent Stochastic Processes With Parametric Uncertainty”, IEEE Trans. Inf. Theory, 62:11 (2016), 6594–6608  crossref  mathscinet  zmath  isi  scopus
    14. Dayanik S., Sezer S.O., “Sequential Sensor Installation for Wiener Disorder Detection”, Math. Oper. Res., 41:3 (2016), 827–850  crossref  mathscinet  zmath  isi  elib  scopus
    15. Yang H., Hadjiliadis O., Ludkovski M., “Quickest Detection in the Wiener Disorder Problem With Post-Change Uncertainty”, Stochastics, 89:3-4 (2017), 654–685  crossref  mathscinet  zmath  isi  scopus
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