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

Research paper by Sergio I. López, Leandro P. R. Pimentel

Indexed on: 07 Nov '16Published on: 07 Nov '16Published in: arXiv - Mathematics - Probability



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.