Table of Contents
Journal of Probability
Volume 2014 (2014), Article ID 786854, 9 pages
http://dx.doi.org/10.1155/2014/786854
Research Article

Wiener-Itô Chaos Expansion of Hilbert Space Valued Random Variables

Ural Federal University, No. 19, Mira Street, Ekaterinburg 620002, Russia

Received 23 November 2013; Accepted 13 February 2014; Published 7 April 2014

Academic Editor: Farrukh Mukhamedov

Copyright © 2014 M. A. Alshanskiy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The notion of -fold iterated Itô integral with respect to a cylindrical Hilbert space valued Wiener process is introduced and the Wiener-Itô chaos expansion is obtained for a square Bochner integrable Hilbert space valued random variable. The expansion can serve a basis for developing the Hilbert space valued analog of Malliavin calculus of variations which can then be applied to the study of stochastic differential equations in Hilbert spaces and their solutions.