The first-passage area for drifted Brownian motion and the moments of the Airy distribution
classification
❄️ cond-mat.stat-mech
math.COmath.PR
keywords
distributionairyareabrowniandriftedfirst-passagemomentsmotion
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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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