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Uspekhi Mat. Nauk, 1996, Volume 51, Issue 4(310), Pages 173–174 (Mi umn1010)  

This article is cited in 53 scientific papers (total in 53 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

Minimax optimality of the method of cumulative sums (cusum) in the case of continuous time

A. N. Shiryaev

Steklov Mathematical Institute, Russian Academy of Sciences

DOI: https://doi.org/10.4213/rm1010

Full text: PDF file (229 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1996, 51:4, 750–751

Bibliographic databases:

MSC: 49K35, 65C30
Accepted: 18.06.1996

Citation: A. N. Shiryaev, “Minimax optimality of the method of cumulative sums (cusum) in the case of continuous time”, Uspekhi Mat. Nauk, 51:4(310) (1996), 173–174; Russian Math. Surveys, 51:4 (1996), 750–751

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Mazalov, VV, “Method of cumulative sums and problems of optimal control by technological processes”, International Journal of Software Engineering and Knowledge Engineering, 7:2 (1997), 219  crossref  mathscinet  isi  elib  scopus  scopus
    2. G. Peskir, A. N. Shiryaev, “On the Brownian First-Passage Time Overa One-Sided Stochastic Boundary”, Theory Probab Appl, 42:3 (1998), 444  mathnet  crossref  mathscinet  zmath  isi
    3. Borovkov, AA, “Asymptotically optimal solutions in the change-point problem”, Theory of Probability and Its Applications, 43:4 (1999), 539  crossref  mathscinet  isi
    4. Brodskii, BE, “Problems and methods of probabilistic diagnostics”, Automation and Remote Control, 60:8 (1999), 1061  mathnet  mathscinet  zmath  isi
    5. Brodskii, BE, “Apriori estimates in change-point problems for random sequence”, Doklady Akademii Nauk, 370:6 (2000), 731  mathnet  mathscinet  isi
    6. Vellekoop, MH, “Optimal speed of detection in generalized Wiener disorder problems”, Stochastic Processes and Their Applications, 95:1 (2001), 25  crossref  mathscinet  zmath  isi  scopus  scopus
    7. A. P. Trifonov, A. V. Zakharov, E. V. Pronyaev, “Adaptive Detection of a Stochastic Signal under Parametric a priori Uncertainty”, Problems Inform. Transmission, 38:3 (2002), 203–217  mathnet  crossref  mathscinet  zmath
    8. Mazalov, VV, “A method of cumulative sums in the problem of detection of traffic changes in computer networks”, Programming and Computer Software, 28:6 (2002), 342  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    9. Shiryaev A.N., “Quickest detection problems in the technical analysis of the financial data”, Mathematical Finance - Bachelier Congress 2000, Springer Finance, 2002, 487–521  crossref  mathscinet  zmath  isi
    10. Theory Probab. Appl., 49:3 (2005), 458–497  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. Moustakides, GV, “Optimality of the CUSUM procedure in continuous time”, Annals of Statistics, 32:1 (2004), 302  crossref  mathscinet  zmath  isi  scopus  scopus
    12. Hadjiliadis, O, “Optimality of the 2-CUSUM drift equalizer rules for detecting two-sided alternatives in the Bownian motion model”, Journal of Applied Probability, 42:4 (2005), 1183  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Brodsky, B, “Asymptotically optimal methods of change-point detection for composite hypotheses”, Journal of Statistical Planning and Inference, 133:1 (2005), 123  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    14. Tartakovsky A.G., “Asymptotic performance of a multichart CUSUM test under false alarm probability constraint”, 44th IEEE Conference on Decision and Control & European Control Conference, 2005, 320–325  crossref  isi  scopus  scopus
    15. Brodsky B., Darkhovsky B., “Asymptotically optimal sequential change-point detection under composite hypotheses”, 44th IEEE Conference on Decision and Control & European Control Conference, 2005, 7347–7351  crossref  isi  scopus  scopus
    16. Theory Probab. Appl., 50:1 (2006), 75–85  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    17. O. Hadjiliadis, J. Vecer, “Drawdowns preceding rallies in the Brownian motion model”, Quantitative Finance, 6:5 (2006), 403–409  crossref  mathscinet  zmath  isi  scopus  scopus
    18. M. Baron, A. G. Tartakovsky, “Asymptotic Optimality of Change-Point Detection Schemes in General Continuous-Time Models”, Sequential Analysis, 25:3 (2006), 257  crossref  mathscinet  zmath
    19. Eugene A. Feinberg, Albert N. Shiryaev, “Quickest detection of drift change for Brownian motion in generalized Bayesian and minimax settings”, stnd, 24:4 (2007), 445  crossref  mathscinet
    20. Arne LØkka, “Detection of disorder before an observable event”, Stochastics An International Journal of Probability and Stochastic Processes, 79:3-4 (2007), 219  crossref  mathscinet  zmath  scopus  scopus
    21. Marianne Frisén, “Properties and Use of the Shewhart Method and Its Followers”, Sequential Analysis, 26:2 (2007), 171  crossref  mathscinet  zmath  scopus  scopus
    22. A. G. Tartakovskii, “Asymptotic Optimality in Bayesian Changepoint Detection Problems under Global False Alarm Probability Constraint”, Theory Probab. Appl., 53:3 (2009), 443–466  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    23. Theory Probab. Appl., 53:3 (2009), 537–547  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    24. A. N. Shiryaev, “On Stochastic Models and Optimal Methods in the Quickest Detection Problems”, Theory Probab. Appl., 53:3 (2009), 385–401  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    25. Andreou, E, “Quality control for structural credit risk models”, Journal of Econometrics, 146:2 (2008), 364  crossref  mathscinet  zmath  isi  scopus  scopus
    26. Moustakides, GV, “Sequential change detection revisited”, Annals of Statistics, 36:2 (2008), 787  crossref  mathscinet  zmath  isi  scopus  scopus
    27. Boris Brodsky, Boris Darkhovsky, “Minimax Methods for Multihypothesis Sequential Testing and Change-Point Detection Problems”, Sequential Analysis, 27:2 (2008), 141  crossref  mathscinet  zmath  elib  scopus  scopus
    28. Olympia Hadjiliadis, Hongzhong Zhang, H. Vincent Poor, “One Shot Schemes for Decentralized Quickest Change Detection”, IEEE Trans Inform Theory, 55:7 (2009), 3346  crossref  mathscinet  zmath  isi  scopus  scopus
    29. Pollak, M, “OPTIMALITY PROPERTIES OF THE SHIRYAEV-ROBERTS PROCEDURE”, Statistica Sinica, 19:4 (2009), 1729  mathscinet  zmath  isi
    30. O. Hadjiliadis, G. Hernandez del-Valle, I. Stamos, “A Comparison of 2-CUSUM Stopping Rules for Quickest Detection of Two-Sided Alternatives in a Brownian Motion Model”, Sequential Analysis, 28:1 (2009), 92  crossref  mathscinet  zmath  scopus  scopus
    31. Dayanik S., “Wiener Disorder Problem with Observations at Fixed Discrete Time Epochs”, Mathematics of Operations Research, 35:4 (2010), 756–785  crossref  mathscinet  zmath  isi  scopus  scopus
    32. Robert Liptser, Alexander Tartakovsky, “From Disorder Detection to Optimal Stopping and Mathematical Finance”, Lsqa, 29:2 (2010), 112  crossref  mathscinet  zmath  elib  scopus  scopus
    33. Moustakides G.V., Polunchenko A.S., Tartakovsky A.G., “A Numerical Approach To Performance Analysis of Quickest Change-Point Detection Procedures”, Stat Sin, 21:2 (2011), 571–596  crossref  mathscinet  zmath  isi  scopus  scopus
    34. Zhang H., Hadjiliadis O., “Quickest Detection in a System with Correlated Noise”, 2012 IEEE 51st Annual Conference on Decision and Control (CDC), IEEE Conference on Decision and Control, IEEE, 2012, 4757–4763  isi
    35. Chronopoulou A., Fellouris G., “Optimal Sequential Change Detection for Fractional Diffusion-Type Processes”, J. Appl. Probab., 50:1 (2013), 29–41  crossref  mathscinet  zmath  isi  scopus  scopus
    36. Mazalov V.V., Nikitina N.N., “A Cusum Method To Detect and Counteract Intrusions”, Program. Comput. Softw., 40:6 (2014), 337–345  crossref  mathscinet  isi  scopus  scopus
    37. Erhan Bayraktar, Lifeng Lai, “Byzantine Fault Tolerant Distributed Quickest Change Detection”, SIAM J. Control Optim, 53:2 (2015), 575  crossref  mathscinet  zmath  scopus  scopus
    38. Zhang H., Rodosthenous N., Hadjiliadis O., “Robustness of the N-Cusum Stopping Rule in a Wiener Disorder Problem”, Ann. Appl. Probab., 25:6 (2015), 3405–3433  crossref  mathscinet  zmath  isi  scopus  scopus
    39. Mijatovic A., Pistorius M., “Asymptotic Independence of Three Statistics of Maximal Segmental Scores”, Statist. Probab. Lett., 99 (2015), 185–191  crossref  mathscinet  zmath  isi  scopus  scopus
    40. Zhang H., “Occupation Times, Drawdowns, and Drawups For One-Dimensional Regular Diffusions”, Adv. Appl. Probab., 47:1 (2015), 210–230  crossref  mathscinet  zmath  isi
    41. A. N. Shiryaev, “On mini-max optimality of CUSUM statistics in change point detection problem for Brownian motion”, Theory Probab. Appl., 61:4 (2017), 719–726  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    42. 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
    43. Polunchenko A.S., “Exact distribution of the Generalized Shiryaev–Roberts stopping time under the minimax Brownian motion setup”, Seq. Anal., 35:1, SI (2016), 108–143  crossref  mathscinet  zmath  isi  elib  scopus
    44. Mijatovic A., Pistorius M., “Joint asymptotic distribution of certain path functionals of the reflected process”, Electron. Commun. Probab., 21 (2016), 43  crossref  mathscinet  zmath  isi  scopus
    45. Polunchenko A.S., Sokolov G., “An Analytic Expression for the Distribution of the Generalized Shiryaev–Roberts Diffusion”, Methodol. Comput. Appl. Probab., 18:4, SI (2016), 1153–1195  crossref  mathscinet  zmath  isi  elib  scopus
    46. 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
    47. Polunchenko A.S., “On the quasi-stationary distribution of the Shiryaev–Roberts diffusion”, Seq. Anal., 36:1 (2017), 126–149  crossref  mathscinet  zmath  isi  scopus
    48. 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  scopus
    49. Johnson P., Moriarty J., Peskir G., “Detecting Changes in Real-Time Data: a User'S Guide to Optimal Detection”, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 375:2100 (2017), 20160298  crossref  mathscinet  isi  scopus  scopus
    50. Krawiec M., Palmowski Z., Plociniczak L., “Quickest Drift Change Detection in Levy-Type Force of Mortality Model”, Appl. Math. Comput., 338 (2018), 432–450  crossref  mathscinet  isi  scopus
    51. Figueroa-Lopez J.E., Olafsson S., “Change-Point Detection For Levy Processes”, Ann. Appl. Probab., 29:2 (2019), 717–738  crossref  mathscinet  isi  scopus
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    53. A. A. Kislitsyn, “Programmnyi kompleks dlya analiza statistiki soglasovannogo urovnya statsionarnosti vremennykh ryadov”, Preprinty IPM im. M. V. Keldysha, 2020, 026, 22 pp.  mathnet  crossref  elib
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