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arXiv · 0811.4485

Second order Poincaré inequalities and CLTs on Wiener space

Ivan Nourdin·Giovanni Peccati·Gesine Reinert
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Abstract

We prove infinite-dimensional second order Poincaré inequalities on Wiener space, thus closing a circle of ideas linking limit theorems for functionals of Gaussian fields, Stein's method and Malliavin calculus. We provide two applications: (i) to a new "second order" characterization of CLTs on a fixed Wiener chaos, and (ii) to linear functionals of Gaussian-subordinated fields.

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Ivan Nourdin, Giovanni Peccati, Gesine Reinert. 2010-02-12. Second order Poincaré inequalities and CLTs on Wiener space. https://arxiv.org/abs/0811.4485

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