Extremes of alpha(t)-locally Stationary Gaussian Random Fields

TL;DR

This paper derives the precise asymptotic behavior of the maximum of alpha(t)-locally stationary Gaussian fields over finite regions, with applications to multifractional Brownian motions and chi-processes.

Contribution

It provides the exact asymptotic formulas for the supremum of alpha(t)-locally stationary Gaussian fields, extending understanding of their extreme value behavior.

Findings

Exact asymptotics for Gaussian field supremum over hypercubes

Asymptotic behavior of multifractional Brownian motion extremes

Results for chi-processes generated by multifractional Brownian motions

Abstract

This contribution derives the exact asymptotic behaviour of the supremum of alpha(t)-locally stationary Gaussian random fields over a finite hypercube. We present two applications of our result; the first one deals with extremes of ggregate multifractional Brownian motions, whereas the second application establishes the exact asymptotics of the supremum of chi-processes generated by multifractional Brownian motions.