The first-passage area for drifted Brownian motion and the moments of the Airy distribution

Abstract

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis also leads to a simple closed-form solution for the moments of the Airy distribution.

13 pages

Cited by in corpus (6)

• On the time to reach maximum for a variety of constrained Brownian motions
• Statistics of the first passage time of Brownian motion conditioned by maximum value or area
• On the joint distribution of first-passage time and first-passage area of drifted Brownian motion
• Maximum relative height of one-dimensional interfaces : from Rayleigh to Airy distribution
• Area distribution and the average shape of a Lévy bridge
• Fragmentation of a sheet by propagating, branching and merging cracks