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April 2017 Quickest detection problems for Bessel processes
Peter Johnson, Goran Peskir
Ann. Appl. Probab. 27(2): 1003-1056 (April 2017). DOI: 10.1214/16-AAP1223


Consider the motion of a Brownian particle that initially takes place in a two-dimensional plane and then after some random/unobservable time continues 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 time at which the particle departs from the plane as accurately as possible. We solve this problem in the most uncertain scenario when the random/unobservable time is (i) exponentially distributed and (ii) independent from the initial motion of the particle in the plane. The solution is expressed in terms of a stopping time that minimises the probability of a false early detection and the expected delay of a missed late detection.


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Peter Johnson. Goran Peskir. "Quickest detection problems for Bessel processes." Ann. Appl. Probab. 27 (2) 1003 - 1056, April 2017.


Received: 1 September 2015; Revised: 1 March 2016; Published: April 2017
First available in Project Euclid: 26 May 2017

zbMATH: 1370.60135
MathSciNet: MR3655860
Digital Object Identifier: 10.1214/16-AAP1223

Primary: 60G40, 60H30, 60J60
Secondary: 35K67, 45G10, 62C10

Rights: Copyright © 2017 Institute of Mathematical Statistics


Vol.27 • No. 2 • April 2017
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