Stable Convergence of Multiple Wiener-Itô Integrals

Giovanni Peccati () and Murad S. Taqqu ()
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Giovanni Peccati: Université Paris VI
Murad S. Taqqu: Boston University

Journal of Theoretical Probability, 2008, vol. 21, issue 3, 527-570

Abstract: 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; 60G60; 60G57; 60F05; 60H05; 60H07 (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-008-0154-x

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