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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

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


Fred Espen Benth


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