Journal of Applied Probability

On the location of the maximum of a continuous stochastic process

Leandro P. R. Pimentel

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


In this short article we will provide a sufficient and necessary condition to have uniqueness of the location of the maximum of a stochastic process over an interval. The result will also express the mean value of the location in terms of the derivative of the expectation of the maximum of a linear perturbation of the underlying process. As an application, we will consider a Brownian motion with variable drift. The ideas behind the method of proof will also be useful to study the location of the maximum, over the real line, of a two-sided Brownian motion minus a parabola and of a stationary process minus a parabola.

Article information

J. Appl. Probab., Volume 51, Number 1 (2014), 152-161.

First available in Project Euclid: 25 March 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G17: Sample path properties
Secondary: 60G10: Stationary processes 60G15: Gaussian processes

Sample path properties maxima argmax Brownian motion stationary process parabolic drift


Pimentel, Leandro P. R. On the location of the maximum of a continuous stochastic process. J. Appl. Probab. 51 (2014), no. 1, 152--161. doi:10.1239/jap/1395771420.

Export citation