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Quickest search over Brownian channels

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In this paper we resolve an open problem proposed by Lai, Vincent Poor, Xin, and Georgiadis [Quickest search over multiple sequences. IEEE Trans. Inf. Theory 57(8) (2011), pp. 5375–5386]. Consider a sequence of Brownian motions with unknown drift equal to one or zero, which may be observed one at a time. We give a procedure for finding, as quickly as possible, a process which is a Brownian motion with non-zero drift. This original quickest search problem, in which the filtration itself is dependent on the observation strategy, is reduced to a single filtration impulse control and optimal stopping problem, which is in turn reduced to an optimal stopping problem for a reflected diffusion, which can be explicitly solved.
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Keywords: Bayesian quickest search; optimal stopping; optimal switching; reflected diffusion

Document Type: Research Article

Affiliations: Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI,48104, USA

Publication date: May 4, 2014

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