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

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

Bibliographic databases:

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
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Dohnal G., Bukovsky I., “Novelty Detection Based on Learning Entropy”, Appl. Stoch. Models. Bus. Ind.
2. Glonti O., “The optimal forecasting for the multinomial scheme with disorder”, Georgian Math. J., 17:2 (2010), 217–228
3. Omar Glonti, Zaza Khechinashvili, “Geometric Gaussian martingales with disorder”, Theory Stoch. Process., 16(32):1 (2010), 44–48
4. B. S. Darhovsky, “Uncertain change-point problem for random sequence”, Theory Probab. Appl., 56:1 (2012), 44–56
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
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
7. B. S. Darhovsky, “Change-point detection in random sequence under minimal prior information”, Theory Probab. Appl., 58:3 (2014), 488–493
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
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
10. Komaee A., “Quickest Detection of a Random Pulse in White Gaussian Noise”, IEEE Trans. Autom. Control, 59:6 (2014), 1468–1479
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
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
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
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
15. Xu Z.Q., Yi F., “Optimal Redeeming Strategy of Stock Loans Under Drift Uncertainty”, Math. Oper. Res., 45:1 (2020), 384–401
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
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