On the maxima of suprema of dependent Gaussian models

TL;DR

This paper investigates the asymptotic behavior of the maximum values of dependent Gaussian processes with trends, revealing different normalization methods depending on the time scale, with applications in queueing systems and extreme value theory.

Contribution

It provides new asymptotic results for maxima of dependent Gaussian processes with trends across various time scales, enhancing understanding of their extreme value behavior.

Findings

Different normalizing functions are identified for various time horizons.

Results have applications in Gaussian queueing system delay estimation.

Insights into extreme value theory for dependent Gaussian arrays.

Abstract

In this paper, we study the asymptotic distribution of the maxima of suprema of dependent Gaussian processes with trend. For different scales of the time horizon we obtain different normalizing functions for the convergence of the maxima. The obtained results not only have potential applications in estimating the delay of certain Gaussian fork-join queueing systems but also provide interesting insights to the extreme value theory for triangular arrays of random variables with row-wise dependence.