Quickest Search over Brownian Channels

Details Quickest Search over Brownian Channels Quickest Search over Brownian Channels

2012-01-08

arxiv.org/abs/1201.1662v1

Mathematics

Probability

Keywords: Bayesian quickest search, optimal switching, optimal stopping, reflected diffusion

Scientific paper

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 \emph{reflected} diffusion, which can be \emph{explicitly} solved.

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