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March 2013 Bayesian quickest detection problems for some diffusion processes
Pavel V. Gapeev, Albert N. Shiryaev
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Adv. in Appl. Probab. 45(1): 164-185 (March 2013). DOI: 10.1239/aap/1363354107

Abstract

We study the Bayesian problems of detecting a change in the drift rate of an observable diffusion process with linear and exponential penalty costs for a detection delay. The optimal times of alarms are found as the first times at which the weighted likelihood ratios hit stochastic boundaries depending on the current observations. The proof is based on the reduction of the initial problems into appropriate three-dimensional optimal stopping problems and the analysis of the associated parabolic-type free-boundary problems. We provide closed-form estimates for the value functions and the boundaries, under certain nontrivial relations between the coefficients of the observable diffusion.

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Pavel V. Gapeev. Albert N. Shiryaev. "Bayesian quickest detection problems for some diffusion processes." Adv. in Appl. Probab. 45 (1) 164 - 185, March 2013. https://doi.org/10.1239/aap/1363354107

Information

Published: March 2013
First available in Project Euclid: 15 March 2013

zbMATH: 1261.62077
MathSciNet: MR3077545
Digital Object Identifier: 10.1239/aap/1363354107

Subjects:
Primary: 34K10, 60G40, 62M20
Secondary: 60J60, 62C10, 62L15

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 1 • March 2013
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