Stable convergence of multiple Wiener-Itô integrals

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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).
31 pages

Keywords

Probability, 60G60, 60G57, 60F05, 60H05, 60H07

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/121540

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604530
 http://arxiv.org/abs/math/0604530

Collections

arXiv