International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 28, Pages 1463-1476

An extension of the Clark-Ocone formula

Said Ngobi1 and Aurel Stan2

1Department of Mathematics and Computer Science, Alabama State University, 915 S. Jackson Street, Montgomery 36101-0271, AL, USA
2Department of Mathematics, University of Rochester, Ray P. Hylan Building, Rochester 14627, NY, USA

Received 21 April 2003

Copyright © 2004 Said Ngobi and Aurel Stan. 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.


A white noise proof of the classical Clark-Ocone formula is first provided. This formula is proven for functions in a Sobolev space which is a subset of the space of square-integrable functions over a white noise space. Later, the formula is generalized to a larger class of operators.