Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 1 (2014), 152-161.
On the location of the maximum of a continuous stochastic process
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.
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
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. https://projecteuclid.org/euclid.jap/1395771420