# Rate of Convergence in the Breuer-Major Theorem via Chaos Expansions

## TL;DR

This paper provides new estimates for convergence rates in the Breuer-Major theorem using advanced probabilistic techniques, enhancing understanding of normal approximation in Gaussian functionals.

## Contribution

It introduces novel bounds for total variation and Wasserstein distances by combining Stein's method, Malliavin calculus, and Wiener chaos expansions.

## Key findings

- Improved convergence rate estimates for the Breuer-Major theorem.
- Enhanced bounds for total variation and Wasserstein distances.
- Application of combined probabilistic techniques to Gaussian functionals.

## Abstract

We show new estimates for the total variation and Wasserstein distances in the framework of the Breuer-Major theorem. The results are based on the combination of Stein's method for normal approximations and Malliavin calculus together with Wiener chaos expansions.