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

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
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