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arXiv · 1201.1662

Quickest Search over Brownian Channels

Erhan Bayraktar·Ross Kravitz
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Abstract

In this paper we resolve an open problem proposed by Lai, Poor, Xin, and Georgiadis (2011, IEEE Transactions on Information Theory). Consider a sequence of Brownian Motions with unknown drift equal to one or zero, which we 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 nonzero 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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Erhan Bayraktar, Ross Kravitz. 2013-06-24. Quickest Search over Brownian Channels. https://arxiv.org/abs/1201.1662

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