The Wiener disorder problem with finite horizon

Gapeev, Pavel V.; Peškir, Goran

doi:10.1016/j.spa.2006.04.005

Cited by 50 publications

(24 citation statements)

References 15 publications

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“…This problem has also been solved in finite horizon (see [2] and the references therein). Books [12,Section 4.2] and [8,Section 21] contain expositions of these results and provide further details and references.…”

Section: Introductionmentioning

confidence: 99%

Sequential testing problems for Bessel processes

Johnson

Peškir

2017

Trans. Amer. Math. Soc.

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Consider the motion of a Brownian particle that takes place either in a twodimensional plane or in the three-dimensional space. Given that only the distance of the particle to the origin is being observed, the problem is to detect the true dimension as soon as possible and with minimal probabilities of the wrong terminal decisions. We solve this problem in the Bayesian formulation under any prior probability of the true dimension when the passage of time is penalised linearly.

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Section: Introductionmentioning

confidence: 99%

Sequential testing problems for Bessel processes

Johnson

Peškir

2017

Trans. Amer. Math. Soc.

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“…Such time-inhomogeneous optimal stopping problems for diffusion processes within a finite horizon setting have been considered in McKean [27], van Moerbeke [42], Jacka [23], Broadie and Detemple [4], Myneni [28], Peskir [33,32], and [18,19] among others (see also Peskir and Shiryaev [36, Chapter VII] and Detemple [14] for an overview and further references). Other time-inhomogeneous optimal stopping problems with infinite time horizon were recently considered in [17].…”

Section: 1mentioning

confidence: 99%

“…The method of solution of these problems was based on the reduction of the associated optimal stopping problems to the equivalent free boundary problems for ordinary (integro-)differential operators and a unique characterization of the Bayesian risks by means of the smooth and continuous fit conditions for the value functions at the optimal stopping boundaries. Further investigations of both problems for observable Wiener processes were studied in [18,19] in the finite horizon setting, and for certain more general time-homogeneous diffusions in [20,21] on infinite time intervals.…”

Section: Introductionmentioning

confidence: 99%

On the sequential testing and quickest change-point detection problems for Gaussian processes

Gapeev

Stoev

2017

Stochastics

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We study the sequential hypothesis testing and quickest change-point (disorder) detection problems with linear delay penalty costs for certain observable time-inhomogeneous Gaussian diffusions and fractional Brownian motions. The method of proof consists of the reduction of the initial problems into the associated optimal stopping problems for onedimensional time-inhomogeneous diffusion processes and the analysis of the associated free boundary problems for partial differential operators. We derive explicit estimates for the Bayesian risk functions and optimal stopping boundaries for the associated weighted likelihood ratios and obtain their exact asymptotic growth rates under large time values.

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“…Отметим, что задача обнаружения момента разладки броуновского движения на отрезке рассматривалась в работе [1], где предполагалось, что момент разладки имеет экспоненциальное распределение.…”

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