Maxima and sum for discrete and continuous time Gaussian processes

Abstract

We study the asymptotic relation among the maximum of continuous weakly and strongly dependent stationary Gaussian process, the maximum of this process sampled at discrete time points, and the partial sum of this process. It is shown that these two extreme values and the sum are asymptotically independent if the grid of the discrete time points is sufficiently sparse and the Gaussian process is weakly dependent, and asymptotically dependent if the grid points are Pickands grids or dense grids.

Keywords

Continuous time process / dependence / discrete time process / extreme value / Gaussian process / sum

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg