An Improved Second-Order Poincaré Inequality for Functionals of Gaussian Fields

Anna Vidotto ()
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Anna Vidotto: Università degli Studi di Roma Tor Vergata

Journal of Theoretical Probability, 2020, vol. 33, issue 1, 396-427

Abstract: Abstract We present an improved version of the second-order Gaussian Poincaré inequality, first introduced in Chatterjee (Probab Theory Relat Fields 143(1):1–40, 2009) and Nourdin et al. (J Funct Anal 257(2):593–609, 2009). These novel estimates are used in order to bound distributional distances between functionals of Gaussian fields and normal random variables. Several applications are developed, including quantitative central limit theorems for nonlinear functionals of stationary Gaussian fields related to the Breuer–Major theorem, improving previous findings in the literature and obtaining presumably optimal rates of convergence.

Keywords: Central limit theorems; Second-order Poincaré inequalities; Gaussian approximation; Isonormal Gaussian processes; Functionals of Gaussian fields; Wigner matrices; 60F05; 60G15; 60H07; 60B20 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10959-019-00883-3

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