Abstract
We present an improved version of the second-order Gaussian Poincare 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
