On Piterbarg theorem for maxima of stationary Gaussian sequences

Abstract

Limit distributions of maxima of dependent Gaussian sequence are different according to the convergence rate of their correlations. For three different conditions on convergence rate of the correlations, in this paper we establish Piterbarg theorem for maxima of stationary Gaussian sequences.

Berman’s inequality under random scaling

“…For S n,k = 1, 1 ≤ k ≤ n almost surely, according to [12], under Condition E we have Below we obtain a more general result for our 2-dimensional setup considering Weibull-type random scaling.…”

The Limit Properties of Maxima of Stationary Gaussian Sequences Subject to Random Replacing

“…Ref. [15] extended the results of (4) to weakly and strongly dependent Gaussian sequences. Let {X n , n ≥ 1} be a sequence of stationary Gaussian variables with correlation function r…”

The maxima and sums of multivariate non-stationary Gaussian sequences

“…In this paper, we show that condition (5) is redundant for (3) and we also deal with the multivariate setting when the sample is subject to random failure. For the extremes properties of the sample subject to random failure, we refer to [4,14,23] and the reference therein. Our method strongly relies on those used by [5,13,14].…”