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March 2014 On the location of the maximum of a continuous stochastic process
Leandro P. R. Pimentel
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J. Appl. Probab. 51(1): 152-161 (March 2014). DOI: 10.1239/jap/1395771420

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.

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Leandro P. R. Pimentel. "On the location of the maximum of a continuous stochastic process." J. Appl. Probab. 51 (1) 152 - 161, March 2014. https://doi.org/10.1239/jap/1395771420

Information

Published: March 2014
First available in Project Euclid: 25 March 2014

zbMATH: 1305.60029
MathSciNet: MR3189448
Digital Object Identifier: 10.1239/jap/1395771420

Subjects:
Primary: 60G17
Secondary: 60G10, 60G15

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 1 • March 2014
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