Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 3, Pages 201-207

On the time of the maximum of Brownian motion with drift

Emannuel Buffet

School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland

Received 1 October 2002; Revised 1 March 2003

Copyright © 2003 Emannuel Buffet. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The distribution of the time at which Brownian motion with drift attains its maximum on a given interval is obtained by elementary methods. The proof depends on a remarkable integral identity involving Gaussian distribution functions.