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Abstract
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Journal of Applied Mathematics and Stochastic Analysis 
Volume 16 (2003), Issue 3, Pages 201-207
doi:10.1155/S1048953303000157

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

Abstract

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.