Stable convergence of multiple Wiener-Itô integrals
Files
First author draft
Date
2008-09-01
Authors
Peccati, Giovanni
Taqqu, Murad S.
Version
First author draft
OA Version
Citation
Giovanni Peccati, Murad S Taqqu. 2008. "Stable convergence of multiple Wiener-Ito integrals." JOURNAL OF THEORETICAL PROBABILITY, Volume 21, Issue 3, pp. 527 - 570 (44). https://doi.org/10.1007/s10959-008-0154-x
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]).