An LpLp-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 LpLp-estimates of the quasilinear stochastic partial differential equations driven by Lévy processes of the type equation(0.1)du=(Lu+F(u))dt+Gk(u)dZtk, where LL is a pseudo-differential operator and ZkZk are independent Lévy processes (k=1,2,⋯)(k=1,2,⋯). The operator LL is random and may depend also on time and space variables. In particular, our results include an LpLp-theory of 2m2m-order SPDEs with coefficients measurable in (ω,t)(ω,t) and continuous in xx.