On the maxima of continuous and discrete time Gaussian order statistics processes

Abstract

In this paper, we study the asymptotic relation between the maximum of acontinuous order statistics process formed by stationary Gaussian processesand the maximum of this process sampled at discrete time points. It is shown that, these two maxima are asymptotically independent when the Gaussian processes are weakly dependent and the discrete points are sufficient sparse, while for other case, these two maxima are asymptotically dependent.

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References in corpus (3)

• On Piterbarg Max-discretisation Theorem for Multivariate Stationary Gaussian Processes
• Piterbarg's max-discretisation theorem for stationary vector Gaussian processes observed on different grids
• On Piterbarg's max-discretisation theorem for homogeneous Gaussian random fields