Second order Poincaré inequalities and CLTs on Wiener space

Details Second order Poincaré inequalities and CLTs on Wiener space Second order Poincaré inequalities and CLTs on Wiener space

2008-11-27

arxiv.org/abs/0811.4485v2

Mathematics

Probability

16 pages. A typo in the statement of Theorem 1.1 has been corrected

Scientific paper

We prove infinite-dimensional second order Poincar\'e 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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