Limit theorems for additive functionals of stationary fields, under integrability assumptions on the higher order spectral densities

TL;DR

This paper establishes central limit theorems for additive functionals of stationary fields by leveraging integrability conditions on higher-order spectral densities, expanding the theoretical understanding of such stochastic processes.

Contribution

It introduces new CLT results for stationary fields based on integrability assumptions on spectral densities, utilizing the Holder-Young-Brascamp-Lieb inequality.

Findings

Proves CLTs under specific spectral density integrability conditions

Utilizes Holder-Young-Brascamp-Lieb inequality for derivations

Provides a theoretical framework for analyzing additive functionals

Abstract

We prove central limit theorems for additive functionals of stationary fields under integrability conditions on the higher-order spectral densities, which are derived using the Holder-Young-Brascamp-Lieb inequality.