Comparison Technique for Highly Dependent Stationary Gaussian Processes

Abstract

Extreme value theory for stationary Gaussian processes crucially depends on comparison techniques. Slepian’s inequality and Berman’s Lemma are two well known comparison techniques that have been used in the independent and midly dependent Gaussian processes. These techniques need extensions to deal with strongly dependent cases. A method (called third comparison technique (TCT) here) was introduced by Mittal and Ylvisaker in 1975. It is explained and illustrated here with examples of various results in the literature dealing with strongly dependent stationary Gaussian processes.