2006/04/25 by Giovanni Peccati, Peccati, Giovanni, Murad S. Taqqu +1
Mathematics · #60F05 #60G57 #60G60 #60H05 #60H07 #Algebraic and Geometric Analysis #FOS: Mathematics #Holomorphic and Operator Theory #Probability (math.PR) #Spectral Theory in Mathematical Physics #math.PR #msc:60F05 #msc:60G57 #msc:60G60 #msc:60H05 #msc:60H07
paper · pdf · doi:10.48550/arxiv.math/0604530
31 pages
arxiv created 2006/04/25 · openalex publication_date 2006/04/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-Itô integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of contraction kernels, realized by means of increasing families of projection operators. We also use an infinite-dimensional Clark-Ocone formula, as well as a version of the correspondence between "abstract" and "concrete" filtered Wiener spaces, in a spirit similar to Üstünel and Zakai (1997).