Second order Poincaré inequalities and CLTs on Wiener space

2008/11/27 by Ivan Nourdin, Nourdin, Ivan, Giovanni Peccati +3 · 2 citations
Economics, Econometrics and Finance · Mathematics · #60F05 #60G15 #60H07 #Advanced Mathematical Physics Problems #FOS: Mathematics #Geometry and complex manifolds #Probability (math.PR) #Stochastic processes and financial applications #math.PR #msc:60F05 #msc:60G15 #msc:60H07

paper · pdf · doi:10.48550/arxiv.0811.4485

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

openalex publication_date 2008/11/27 · arxiv created 2010/02/12 · arxiv updated 2010/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• McKean-Vlasov limits of scaling-critical reaction-diffusion equations with random initial data
• Functional second-order Gaussian Poincaré inequalities

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