  Consider the motion of a Brownian particle in three dimensions, whose two
spatial coordinates are standard Brownian motions with zero drift, and the
remaining (unknown) spatial coordinate is a standard Brownian motion with a
non-zero drift. Given that the position of the Brownian particle is being
observed in real time, the problem is to detect as soon as possible and with
minimal probabilities of the wrong terminal decisions, which spatial coordinate
has the non-zero drift. We solve this problem in the Bayesian formulation,
under any prior probabilities of the non-zero drift being in any of the three
spatial coordinates, when the passage of time is penalised linearly. Finding
the exact solution to the problem in three dimensions, including a rigorous
treatment of its non-monotone optimal stopping boundaries, is the main
contribution of the present paper. To our knowledge this is the first time that
such a problem has been solved in the literature.
