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.

arXiv comment13 pages

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• DNA breathing dynamics: Analytic results for distribution functions of relevant Brownian functionals
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• Counting observables in stochastic excursions
• Framework for fluctuating times and counting observables in stochastic excursions
• Short-time large deviations of first-passage functionals for high-order stochastic processes