The maximum of Brownian motion with parabolic drift

Details The maximum of Brownian motion with parabolic drift The maximum of Brownian motion with parabolic drift

2010-02-02

arxiv.org/abs/1002.0497v1

Mathematics

Probability

37 pages

Scientific paper

We study the maximum of a Brownian motion with a parabolic drift; this is a
random variable that often occurs as a limit of the maximum of discrete
processes whose expectations have a maximum at an interior point. We give
series expansions and integral formulas for the distribution and the first two
moments, together with numerical values to high precision.

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