A Sobolev space theory for parabolic stochastic PDEs driven by Lévy processes on ^{C 1}-domains

In this paper we study parabolic stochastic partial differential equations (SPDEs) driven by Lévy processes defined on R^d, R+d and bounded ^C1-domains. The coefficients of the equations are random functions depending on time and space variables. Existence and uniqueness results are proved in (weighted) Sobolev spaces, and ^Lp-estimates and various properties of solutions are also obtained. The number of derivatives of the solutions can be any real number, in particular it can be negative or fractional.