The first-passage area for drifted Brownian motion and the moments of the Airy distribution
Michael J. Kearney, Satya N. Majumdar, and Richard J. Martin
TL;DR
This paper derives an exact distribution for the area under a drifted Brownian motion until its first passage, analyzes asymptotic behavior, and provides a closed-form solution for the Airy distribution's moments.
Contribution
It introduces a novel exact distribution formula for the first-passage area of drifted Brownian motion and a closed-form for the Airy distribution's moments.
Findings
Confirmed asymptotic behavior matches earlier conjectures
Derived a closed-form expression for Airy distribution moments
Provided insights into the distribution of first-passage areas
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.
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