Second order Poincaré inequalities and CLTs on Wiener space

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• 作者：Ivan Nourdin ; Giovanni Peccati ; Gesine Reinert
• 关键词：Central limit theorems ; Isonormal Gaussian processes ; Linear functionals ; Multiple integrals ; Second order Poincaré ; inequalities ; Stein's method ; Wiener chaos
• 刊名：Journal of Functional Analysis
• 出版年：2009
• 出版时间：15 July 2009
• 年：2009
• 卷：257
• 期：2
• 页码：593-609
• 全文大小：193 K

文摘

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.