International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 25-28, Pages 1463-1476
doi:10.1155/S0161171204304230
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
Abstract
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.