  A famous result of Orey and Taylor gives the Hausdorff dimension of the set
of fast times, that is the set of points where linear Brownian motion moves
faster than according to the law of iterated logarithm. In this paper we
examine what happens to the set of fast times if a variable drift is added to
linear Brownian motion. In particular, we will show that the Hausdorff
dimension of the set of fast times cannot be decreased by adding a function to
Brownian motion.
