Second order Poincar\'e inequalities and CLTs on Wiener space
Probability
2010-02-12 v2
Abstract
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.
Cite
@article{arxiv.0811.4485,
title = {Second order Poincar\'e inequalities and CLTs on Wiener space},
author = {Ivan Nourdin and Giovanni Peccati and Gesine Reinert},
journal= {arXiv preprint arXiv:0811.4485},
year = {2010}
}
Comments
16 pages. A typo in the statement of Theorem 1.1 has been corrected