The maximum of Brownian motion minus a parabola
Probability
2010-11-19 v1
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.
Keywords
Cite
@article{arxiv.1011.0022,
title = {The maximum of Brownian motion minus a parabola},
author = {Piet Groeneboom},
journal= {arXiv preprint arXiv:1011.0022},
year = {2010}
}
Comments
7 pages, 4 figures, to appear in the Electronic Journal of Probability