Journal of Applied Probability

On the location of the maximum of a continuous stochastic process

Leandro P. R. Pimentel

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Abstract

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

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

Dates
First available in Project Euclid: 25 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jap/1395771420

Digital Object Identifier
doi:10.1239/jap/1395771420

Mathematical Reviews number (MathSciNet)
MR3189448

Zentralblatt MATH identifier
1305.60029

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

Keywords
Sample path properties maxima argmax Brownian motion stationary process parabolic drift

Citation

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


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