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

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