An L_p-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order

In this article we present uniqueness, existence, and L_p-estimates of the quasilinear stochastic partial differential equations driven by Lévy processes of the type du=(Lu+F(u))dt+G^k(u)dZ_t^k, where L is a pseudo-differential operator and Z^k are independent Lévy processes (k=1,2,⋯). The operator L is random and may depend also on time and space variables. In particular, our results include an L_p-theory of 2m-order SPDEs with coefficients measurable in (ω,t) and continuous in x.