# Probability that the maximum of the reflected Brownian motion over a finite interval [0; t] is achieved by its last zero before t

- Authors
- Publication Date
- Sep 08, 2015
- Source
- HAL-UPMC
- Keywords
- Language
- English
- License
- Unknown
- External links

## Abstract

Probability that the maximum of the reflected Brownian motion over a finite interval [0, t] is achieved by its last zero before t Abstract We calculate the probability pc that the maximum of a reflected Brownian motion U is achieved on a complete excursion, i.e. pc := P U (t) = U * (t) where U (t) (respectively U * (t)) is the maximum of the process U over the time interval [0, t] (resp. 0, g(t) where g(t) is the last zero of U before t).