Statistics of the first passage time of Brownian motion conditioned by   maximum value or area
  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. 
Michael J. Kearney and Satya N. Majumdar
cond-mat.stat-mech math-ph math.MP