On asymptotic constants in the theory of extremes for Gaussian processes

TL;DR

This paper introduces a new representation of Pickands' constants for Gaussian process extremes, enabling reliable estimation algorithms and providing detailed error analysis to validate the approach.

Contribution

It presents a novel representation of Pickands' constants and a reliable estimation algorithm with comprehensive error analysis.

Findings

New representation of Pickands' constants

Reliable estimation algorithm developed

Error analysis confirms approach validity

Abstract

This paper gives a new representation of Pickands' constants, which arise in the study of extremes for a variety of Gaussian processes. Using this representation, we resolve the long-standing problem of devising a reliable algorithm for estimating these constants. A detailed error analysis illustrates the strength of our approach.