Berry-Esseen bounds in the Breuer-Major CLT and Gebelein's inequality

DOI10.1214/19-ECP241arXiv1812.08838MaRDI QIDQ6311468

Xiaochuan Yang, Giovanni Peccati, Ivan Nourdin

Publication date: 20 December 2018

Abstract: 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.

Mathematics Subject Classification ID

Gaussian processes (60G15) Central limit and other weak theorems (60F05) Stochastic calculus of variations and the Malliavin calculus (60H07)

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