Statistics of the first passage time of Brownian motion conditioned by maximum value or area

Michael J. Kearney ¹ Satya N. Majumdar ²

Journal of Physics A: Mathematical and Theoretical, Institute of Physics: Hybrid Open Access, 2014, 47, pp.465001

We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated.

• 1. Faculty of Engineering and Physical Sciences
• 2. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques