On the rate of convergence for central limit theorems of sojourn times of Gaussian fields

TL;DR

This paper investigates the convergence rates in central limit theorems for sojourn times of Gaussian fields, utilizing Malliavin calculus and Stein's method, and extends existing results to multidimensional cases.

Contribution

It introduces a novel approach to quantify convergence rates for Gaussian field sojourn times and extends Berman's results to higher dimensions.

Findings

Established convergence rate bounds for fixed and moving levels

Extended Berman's results to multidimensional Gaussian fields

Demonstrated effectiveness of Malliavin calculus and Stein's method in this context

Abstract

The aim of this paper is to control the rate of convergence for central limit theorems of sojourn times of Gaussian fields in both cases: the fixed and the moving level. Our main tools are the Malliavin calculus and the Stein's method, developed by Nualart, Peccati and Nourdin. We also extend some results of Berman to the multidimensional case.