Centre for Mathematical Physics and Stochastics

Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 1998-17

September 1998

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.

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