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Journal of Theoretical Probability

, Volume 21, Issue 3, pp 527–570 | Cite as

Stable Convergence of Multiple Wiener-Itô Integrals

  • Giovanni Peccati
  • Murad S. Taqqu
Article

Abstract

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. Note that stable convergence is stronger than convergence in distribution. 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 that of Üstünel and Zakai (J. Funct. Anal. 143, 10–32, [1997]).

Keywords

Stable convergence Multiple Wiener-Itô integrals Projection operators Gaussian processes 

Mathematics Subject Classification (2000)

60G60 60G57 60F05 60H05 60H07 

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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Laboratoire de Statistique Théorique et AppliquéeUniversité Paris VIParisFrance
  2. 2.Department of MathematicsBoston UniversityBostonUSA

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