Electronic Communications in Probability

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

Ivan Nourdin, Giovanni Peccati, and Xiaochuan Yang

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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.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 34, 12 pp.

Received: 10 February 2019
Accepted: 10 May 2019
First available in Project Euclid: 22 June 2019

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Zentralblatt MATH identifier

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

Breuer-Major theorem rate of convergence Gebelein’s inequality Malliavin-Stein approach

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Nourdin, Ivan; Peccati, Giovanni; Yang, Xiaochuan. Berry-Esseen bounds in the Breuer-Major CLT and Gebelein’s inequality. Electron. Commun. Probab. 24 (2019), paper no. 34, 12 pp. doi:10.1214/19-ECP241. https://projecteuclid.org/euclid.ecp/1561169050

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