Probability distributions of extremes of self-similar Gaussian random fields

TL;DR

This paper derives upper bounds for the probability distributions of extreme values in self-similar Gaussian random fields with stationary increments, providing insights into their behavior on compact spaces.

Contribution

It introduces new upper bounds for the extremes of self-similar Gaussian fields with stationary increments on compact spaces, expanding understanding of their probabilistic properties.

Findings

Derived upper bounds for probability distributions of extremes.

Analyzed normalized self-similar Gaussian fields in .

Applied classical series analysis techniques.

Abstract

We have obtained some upper bounds for the probability distribution of extremes of a self-similar Gaussian random field with stationary rectangular increments that are defined on the compact spaces. The probability distributions of extremes for the normalized self-similar Gaussian random fields with stationary rectangular increments defined in ${\mathbb{R}}^2_+$ have been presented. In our work we have used the techniques developed for the self-similar fields and based on the classical series analysis of the maximal probability bounding from below for the Gaussian fields.