The maximum of a strongly correlated Gaussian process

TL;DR

This paper extends the understanding of the maximum behavior of Gaussian processes, relaxing previous conditions for Gaussian limits and applying to smooth non-stationary fields.

Contribution

It introduces a new approach that broadens the conditions under which the maximum of Gaussian processes converges to a Gaussian limit, including non-stationary fields.

Findings

Relaxed conditions for Gaussian limit of maxima

Extended results to non-stationary Gaussian fields

Provided a new proof approach

Abstract

We revisit a result of Mittal--Ylvisaker that states that the rescaled maximum of a stationary sequence of Gaussian random variables has a Gaussian limit if correlations decay sufficiently slowly. Taking a new approach we relax the conditions for the Gaussian limit and give an extension to smooth non-stationary random fields.