Functional second-order Gaussian Poincar\'e inequalities
Abstract
In this paper, we work in the framework of Hilbert-valued Wiener structures and derive a functional version of the second-order Gaussian Poincar\'e inequality that leads to abstract bounds for Gaussian process approximation in d2 distance. Our abstract bounds are flexible and can be applied in various examples including functional Breuer-Major central limit theorems, shallow neural networks, and spatial statistics of SPDEs solutions.
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