Harnack inequalities for SDEs driven by cylindrical $\alpha$-stable processes

Abstract

By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular, cylindrical $\alpha$-stable processes). Moreover, the gradient estimate is also derived when the drift is Lipschitz continuous.