SDE solutions in the space of smooth random variables

Abstract

In this paper we analyze properties of a dual pair (G;G ) of spaces of smooth and generalized random variables on a L evy white noise space. We show that G L 2 ( ) which shares properties with a Fr echet algebra contains a larger class of solutions of It^ o equations driven by pure jump L evy processes. Further a characterization of ( G;G ) in terms of the S-transform is given. We propose (G;G ) as an attractive alternative to the Meyer-Watanabe test function and distribution space (D1;D1 ) (W) to study strong solutions of SDE's.