Michael J. Kearney 1, Satya N. Majumdar 2, Richard J. Martin 3
Journal of Physics A Mathematical and Theoretical 40 (2007) F863
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.
- 1. Faculty of Engineering and Physical Sciences,
University of Surrey - 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI – Paris Sud - 3. Quantitative Credit Strategy Group,
Credit suisse