  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.
