arXiv:0811.4485 Abstract | arXiv Analytics

arXiv:0811.4485 [math.PR]Abstract References Reviews Resources

Second order Poincaré inequalities and CLTs on Wiener space

Ivan Nourdin, Giovanni Peccati, Gesine Reinert

Published 2008-11-27, updated 2010-02-12Version 2

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.

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

Categories: math.PR

Subjects: 60F05, 60G15, 60H07

Keywords: wiener space, infinite-dimensional second order poincare inequalities, ideas linking limit theorems, linear functionals, gaussian fields

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