Berry-Esseen type estimates for nonconventional sums

TL;DR

This paper derives Berry-Esseen type bounds for nonconventional sums involving dependent random variables, extending classical central limit theorem estimates to more complex, structured sums.

Contribution

It introduces new Berry-Esseen estimates specifically for nonconventional sums, broadening the scope of probabilistic limit theorems.

Findings

Established Berry-Esseen bounds for nonconventional sums

Extended classical CLT estimates to dependent, structured sums

Provided quantitative convergence rates in the nonconventional setting

Abstract

We obtain Berry-Esseen type estimates for "nonconventional" expressions of the form $\xi_N=\frac 1{\sqrt N}\sum_{n=1}^N(F(X(q_1(n)),...,X(q_\ell(n)))-\bar F)$