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

Abstract

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.

29 pages, 4 figures included

References in corpus (2)

• On the time to reach maximum for a variety of constrained Brownian motions
• The first-passage area for drifted Brownian motion and the moments of the Airy distribution

Cited by in corpus (7)

• Extreme value statistics of correlated random variables: a pedagogical review
• Statistics of first-passage Brownian functionals
• Statistics of the first passage area functional for an Ornstein-Uhlenbeck process
• First-passage functionals for Ornstein Uhlenbeck process with stochastic resetting
• Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime
• On the area swept by a biased diffusion till its first-exit time: Martingale approach and gambling opportunities
• Concentration of Empirical First-Passage Times