We derive explicit Berry-Esseen bounds in the total variation distance for the Breuer-Major central limit theorem, in the case of a subordinating function $\varphi $ satisfying minimal regularity assumptions. Our approach is based on the combination of the Malliavin-Stein approach for normal approximations with Gebelein’s inequality, bounding the covariance of functionals of Gaussian fields in terms of maximal correlation coefficients.
"Berry-Esseen bounds in the Breuer-Major CLT and Gebelein’s inequality." Electron. Commun. Probab. 24 1 - 12, 2019. https://doi.org/10.1214/19-ECP241