Stable convergence of multiple Wiener-Itô integrals

Giovanni Peccati; Murad S. Taqqu

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Stable convergence of multiple Wiener-Itô integrals

Giovanni Peccati·Murad S. Taqqu

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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. 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).

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Giovanni Peccati, Murad S. Taqqu. 2006-04-25. Stable convergence of multiple Wiener-Itô integrals. https://arxiv.org/abs/math/0604530

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