Harnack inequalities for stochastic equations driven by Levy noise

By using coupling argument and regularization approximations of the underlying sub-ordinator, dimension-free Harnack inequalities are established for a class of stochastic equations driven by a Levy noise containing a subordinate Brownian motion. The Harnack inequalities are new even for linear equations driven by Levy noise, and the gradient estimate implied by our log-Harnack inequality considerably generalizes some recent results on gradient estimates and coupling properties derived for Levy processes or linear equations driven by Levy noise. The main results are also extended to semilinear stochastic equations in Hilbert spaces. (C) 2013 Elsevier Inc. All rights reserved.