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Teor. Veroyatnost. i Primenen., 2008, Volume 53, Issue 3, Pages 417–436 (Mi tvp2429)  

This article is cited in 16 scientific papers (total in 16 papers)

On Stochastic Models and Optimal Methods in the Quickest Detection Problems

A. N. Shiryaev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: This paper is an introduction to the thematic issue devoted to the optimal and asymptotically optimal methods of decision making in problems of the quickest detection of changes of probability characteristics of observed processes (the “disorder” problem), as well as some general problems of the optimal stopping theory on which the decision of these problems is based. This paper's introductory purpose is twofold: on the one hand it gives a general model covering a variate of schemes describing the appearance of disorder, and on the other hand it describes briefly the specific models and general problems concerning the optimal stopping theory which the papers of this issue contain.

Keywords: control charts procedure, CUSUM-method, quickest detection problem, $\theta$-model, Bayesian $G$-model, stopping times, optimal stopping rules.

DOI: https://doi.org/10.4213/tvp2429

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English version:
Theory of Probability and its Applications, 2009, 53:3, 385–401

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Received: 19.03.2008

Citation: A. N. Shiryaev, “On Stochastic Models and Optimal Methods in the Quickest Detection Problems”, Teor. Veroyatnost. i Primenen., 53:3 (2008), 417–436; Theory Probab. Appl., 53:3 (2009), 385–401

Citation in format AMSBIB
\by A.~N.~Shiryaev
\paper On Stochastic Models and Optimal Methods in the Quickest Detection Problems
\jour Teor. Veroyatnost. i Primenen.
\yr 2008
\vol 53
\issue 3
\pages 417--436
\jour Theory Probab. Appl.
\yr 2009
\vol 53
\issue 3
\pages 385--401

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    This publication is cited in the following articles:
    1. Dohnal G., Bukovsky I., “Novelty Detection Based on Learning Entropy”, Appl. Stoch. Models. Bus. Ind.  crossref  isi
    2. Glonti O., “The optimal forecasting for the multinomial scheme with disorder”, Georgian Math. J., 17:2 (2010), 217–228  mathscinet  zmath  isi
    3. Omar Glonti, Zaza Khechinashvili, “Geometric Gaussian martingales with disorder”, Theory Stoch. Process., 16(32):1 (2010), 44–48  mathnet  mathscinet  zmath
    4. B. S. Darhovsky, “Uncertain change-point problem for random sequence”, Theory Probab. Appl., 56:1 (2012), 44–56  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    5. Polunchenko A.S. Tartakovsky A.G., “State-of-the-art in sequential change-point detection”, Methodol. Comput. Appl. Probab., 14:3 (2012), 649–684  crossref  mathscinet  zmath  isi  elib  scopus
    6. Kenett R.S., Pollak M., “On assessing the performance of sequential procedures for detecting a change”, Qual. Reliab. Eng. Int., 28:5 (2012), 500–507  crossref  mathscinet  isi  elib  scopus
    7. 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
    8. B. S. Darhovsky, A. Piryatinska, “New approach to the segmentation problem for time series of arbitrary nature”, Proc. Steklov Inst. Math., 287:1 (2014), 54–67  mathnet  crossref  crossref  isi  elib  elib
    9. Fontana C., Grbac Z., Jeanblanc M., Li Q., “Information, No-Arbitrage and Completeness For Asset Price Models With a Change Point”, Stoch. Process. Their Appl., 124:9 (2014), 3009–3030  crossref  mathscinet  zmath  isi  elib  scopus
    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. Darkhovsky B., Piryatinska A., “Quickest Detection of Changes in the Generating Mechanism of a Time Series Via the Epsilon-Complexity of Continuous Functions”, Seq. Anal., 33:2 (2014), 231–250  crossref  mathscinet  zmath  isi  elib  scopus
    12. Ferenstein E.Z., Pasternak-Winiarski A., “Mathematical model of detecting disorders in service systems”, 2015 20th International Conference on Methods and Models in Automation and Robotics (MMAR ) (Miedzyzdroje, Poland), IEEE, 2015, 724–727  crossref  isi  scopus
    13. Lao D., Sundaramoorthi G., “Minimum Delay Moving Object Detection”, 30Th IEEE Conference on Computer Vision and Pattern Recognition (Cvpr 2017), IEEE Conference on Computer Vision and Pattern Recognition, IEEE, 2017, 4809–4818  crossref  isi  scopus
    14. El Karoui N., Loisel S., Salhi Ya., “Minimax Optimality in Robust Detection of a Disorder Time in Doubly-Stochastic Poisson Processes”, Ann. Appl. Probab., 27:4 (2017), 2515–2538  crossref  mathscinet  zmath  isi  scopus
    15. Xu Z.Q., Yi F., “Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty”, Math. Oper. Res., 45:1 (2020), 384–401  crossref  mathscinet  isi
    16. Ding S. Li X. Dong X. Yang W., “The Consistency of the Cusum-Type Estimator of the Change-Point and Its Application”, Mathematics, 8:12 (2020), 2113  crossref  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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