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Second order Poincaré inequalities and CLTs on Wiener space |
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| Authors: | Ivan Nourdin Gesine Reinert |
| Institution: | a Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie (Paris VI), Boîte courrier 188, 4 place Jussieu, 75252 Paris, Cedex 05, France b Equipe Modal'X, Université Paris Ouest - Nanterre la Défense, 200 Avenue de la République, 92000 Nanterre, France c LSTA, Université Paris VI, France d Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK |
| 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. |
| Keywords: | Central limit theorems Isonormal Gaussian processes Linear functionals Multiple integrals Second order Poincaré inequalities Stein's method Wiener chaos |
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