The maximum of Brownian motion minus a parabola.

Authors: Piet Groeneboom
Subjects: Probability
link: http://arxiv.org/abs/1011.0022
Abstract

We derive a simple integral representation for the distribution of the
maximum of Brownian motion minus a parabola, which can be used for computing
the density and moments of the distribution, both for one-sided and two-sided
Brownian motion.