An $L^p$-theory of non-divergence form SPDEs driven by L\'evy processes

Abstract

In this paper we present an $L^p$-theory for the stochastic partial differential equations (SPDEs in abbreciation) driven by L\'e{}vy processes. Existence and uniqueness of solutions in Sobolev spaces are obtained. The coefficients of SPDEs under consideration are random functions depending on time and space variables.