Weak convergence of weighted additive functionals of long-range dependent fields

TL;DR

This paper investigates the asymptotic distribution of weighted nonlinear functionals of long-range dependent Gaussian fields, showing their equivalence to integral functionals under certain conditions, with applications to multidimensional integrals.

Contribution

It provides new asymptotic results for weighted nonlinear functionals of Gaussian fields with long-range dependence and establishes their distributional equivalence to integral functionals.

Findings

Asymptotic distribution results for weighted nonlinear functionals

Equivalence of integral and additive functionals under certain conditions

Application to multidimensional rectangle integrals

Abstract

We provide asymptotic results for the distribution of weighted nonlinear functionals of Gaussian field with long-range dependence. We also show that integral functionals and the corresponding additive functionals have same distributions under certain assumptions. The result is applied to integrals over a multidimensional rectangle with a constant weight function.