A note on fast times of Brownian motion with variable drift

Details A note on fast times of Brownian motion with variable drift A note on fast times of Brownian motion with variable drift

2012-03-04

arxiv.org/abs/1203.0752v1

Mathematics

Probability

17 pages

Scientific paper

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.

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