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arXiv · 1207.4469

On the location of the maximum of a continuous stochastic process

Leandro P. R. Pimentel
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Abstract

In this short note 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. 2012-07-18. On the location of the maximum of a continuous stochastic process. https://arxiv.org/abs/1207.4469

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