Stable convergence of multiple Wiener-Itô integrals

Details Stable convergence of multiple Wiener-Itô integrals Stable convergence of multiple Wiener-Itô integrals

2006-04-25

arxiv.org/abs/math/0604530v1

Mathematics

Probability

31 pages

Scientific paper

We prove sufficient conditions, ensuring that a sequence of multiple Wiener-It\^{o} 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 \"{U}st\"{u}nel and Zakai (1997).

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