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

DOI10.1214/19-ECP241MaRDI QIDQ2316568

Ivan Nourdin, Xiaochuan Yang, Giovanni Peccati

Publication date: 6 August 2019

Published in: Electronic Communications in Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1812.08838

zbMATH Keywords

rate of convergenceMalliavin-Stein approachGebelein's inequalityBreuer-major theorem

Mathematics Subject Classification ID

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

Related Items (9)

Fourth moment bound and stationary Gaussian processes with positive correlation ⋮ AR(1) processes driven by second-chaos white noise: Berry-Esséen bounds for quadratic variation and parameter estimation ⋮ Besov-Orlicz path regularity of non-Gaussian processes ⋮ Malliavin-Stein method: a survey of some recent developments ⋮ Oscillating Gaussian processes ⋮ Approximation of Hilbert-valued gaussians on Dirichlet structures ⋮ Rate of convergence in the Breuer-Major theorem via chaos expansions ⋮ Multivariate normal approximation on the Wiener space: new bounds in the convex distance ⋮ How does tempering affect the local and global properties of fractional Brownian motion?

Cites Work

• Quantitative Breuer-Major theorems
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• Parameter estimation for fractional Ornstein-Uhlenbeck processes
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• Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems
• Stochastic models for time series
• Convergence in total variation on Wiener chaos
• Total variation estimates in the Breuer-Major theorem
• Continuous Breuer-Major theorem: tightness and nonstationarity
• An improved second-order Poincaré inequality for functionals of Gaussian fields
• Nodal statistics of planar random waves
• Analysis of Variations for Self-similar Processes
• Lectures on Gaussian Approximations with Malliavin Calculus
• Normal Approximations with Malliavin Calculus
• Reversing the Berry-Esseen Inequality
• The Malliavin Calculus and Related Topics
• Convergence of integrated processes of arbitrary Hermite rank
• Introduction to Malliavin Calculus
• The optimal fourth moment theorem
• Long-Range Dependence and Self-Similarity

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