Limit Laws for Maxima of Contracted Stationary Gaussian Sequences

Abstract

The principal results of this contribution are the weak and strong limits of maxima of contracted stationary Gaussian random sequences. Due to the random contraction we introduce a modified Berman condition which is sufficient for the weak convergence of the maxima of the scaled sample. Under a stronger assumption the weak convergence is strengthened to almost convergence.

Keywords:

• Davis–Resnick tail property
• Gumbel max-domain of attraction
• Random contraction
• Stationary Gaussian sequence.

Mathematics Subject Classification:

• Primary: 60F05; Secondary: 60G15