On the location of the maximum of a process: L\'evy, Gaussian and multidimensional cases

Abstract

In this short article we show how the techniques presented in arXiv:1207.4469 can be extended to a variety of non continuous and multivariate processes. As examples, we prove uniqueness of the location of the maximum for spectrally positive L\'evy processes, Ornstein-Uhlenbeck process, fractional Brownian Motion and the Brownian sheet among others gaussian processes.