MPS-RR 1998-17
September 1998

On weighted $L^2(Omega)$-Spaces, their Duals and Ito Integration

by:

Fred Espen Benth

Abstract

We construct spaces of smooth and generalized random variables which can be considered as weighted $L^2(Omega)$-spaces. Ito integration for generalized stochastic processes is defined. The construction follows closely the standard $L^2(Omega)$-case, except for the norms which are weighted. As an application of our results, we derive a Clark-Ocone formula.

Availability: [ gzipped ps-file ] [ pdf-file ]

[ Help on down-loading/viewing/printing ]

This paper has now been published in Stochastic Analysis and Applications, Vol 19 (3), 779-799 (2001)