# On rate of convergence in non-central limit theorems

## TL;DR

This paper establishes the rate of convergence to Hermite-type distributions in non-central limit theorems, providing novel results for functionals of random fields with higher Hermite ranks under general spectral density conditions.

## Contribution

It presents the first known rates of convergence for functionals of random fields to Hermite-type distributions with ranks greater than 2, under weak spectral density assumptions.

## Key findings

- Derived convergence rates for Hermite-type distributions
- Analyzed Lévy concentration functions for these distributions
- Extended results to higher Hermite ranks

## Abstract

The main result of this paper is the rate of convergence to Hermite-type distributions in non-central limit theorems. To the best of our knowledge, this is the first result in the literature on rates of convergence of functionals of random fields to Hermite-type distributions with ranks greater than 2. The results were obtained under rather general assumptions on the spectral densities of random fields. These assumptions are even weaker than in the known convergence results for the case of Rosenblatt distributions. Additionally, L\'{e}vy concentration functions for Hermite-type distributions were investigated.