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

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

2007-06-14

arxiv.org/abs/0706.2038v1

J. Phys. A: Math. Theor. 40, F863 (2007).

Physics

Condensed Matter

Statistical Mechanics

13 pages

Scientific paper

10.1088/1751-8113/40/36/F03

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.

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