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A problem of the fastest detection of regime changing for Levy processes. (English. Russian original) Zbl 1304.60056

Mosc. Univ. Math. Bull. 64, No. 2, 84-86 (2009); translation from Vest. Mosk. Univ. Mat. Mekh. 64, No. 2, 69-71 (2009).
Summary: The optimal stopping time for the fastest regime change (disorder) detection problem in the generalized Bayesian setting is determined for an arbitrary Levy process.

MSC:

60G51 Processes with independent increments; Lévy processes
62L15 Optimal stopping in statistics
62C10 Bayesian problems; characterization of Bayes procedures
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References:

[1] E. A. Feinberg and A. N. Shiryaev, ”Quickest Detection of Drift Change for Brownian Motion in Generalized Bayesian and Minimax Settings,” Statistics and Decisions 24(4), 445 (2006). · Zbl 1135.60024 · doi:10.1524/stnd.2006.24.4.445
[2] E. V. Burnaev, ”Disorder Problem for a Poisson Process in the Generalized Bayesian Setting,” Uspekhi Matem. Nauk 62(4), 151, (2007) [Russ. Math. Surveys 62 (4), 790 (2007)]. · Zbl 1136.62055 · doi:10.4213/rm6810
[3] J. Jacod and A. N. Shiryaev, Limit Theorems for Stochastic Processes, (Springer-Verlag, Berlin, 1987). · Zbl 0635.60021
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