An L-p-theory for stochastic partial differential equations driven by Levy processes with pseudo-differential operators of arbitrary order

Abstract

In this article we present uniqueness, existence, and L-p-estimates of the quasilinear stochastic partial differential equations driven by Levy processes of the type du = (Lu + F(u))dt + G(k)(u)dZ(t)(k), (0.1) where L is a pseudo-differential operator and Z(k) are independent Levy 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 (omega, t) and continuous in x. (C) 2016 Elsevier B.V. All rights reserved.