Stable convergence of multiple Wiener-It\^{o} integrals
概率论
2007-05-23 v1
摘要
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).
引用
@article{arxiv.math/0604530,
title = {Stable convergence of multiple Wiener-It\^{o} integrals},
author = {Giovanni Peccati and Murad S. Taqqu},
journal= {arXiv preprint arXiv:math/0604530},
year = {2007}
}
备注
31 pages