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On homogeneous chaos

Published online by Cambridge University Press:  24 October 2008

Nigel Cutland  and
Siu-Ah Ng
Nigel Cutland
Affiliation:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX
Siu-Ah Ng
Affiliation:
Department of Pure Mathematics, University of Hull, Hull HU6 7RX
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Abstract

This paper discusses the Wiener–Itô chaos decomposition of an L2 function φ over Wiener space, and is concerned in particular with the identification of the integrands ƒn in the chaos decomposition

First these are identified as Radon–Nikodým derivatives. Two elementary non-standard proofs of the Wiener–Itô chaos decomposition are given, based on Anderson's construction of Brownian motion and Itô integration.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 110 , Issue 2 , September 1991 , pp. 353 - 363
Copyright
Copyright © Cambridge Philosophical Society 1991

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