On the location of the maximum of a continuous stochastic process

• Autores: Leandro E. R. Pimentel
• Localización: Journal of Applied Probability, ISSN-e 0021-9002, Vol. 51, Nº. 1, 2014, págs. 152-161
• Idioma: inglés
• DOI: 10.1017/s0021900200010147
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• Resumen

  • 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