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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1561169050

Digital Object Identifier
doi:10.1214/19-ECP241

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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References

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