Existence of densities for stable-like driven SDE’s with Hölder continuous coefficients

Consider a multidimensional stochastic differential equation driven by a stable-like Lévy process. We prove that the law of the solution immediately has a density in some Besov space, under some nondegeneracy condition on the driving Lévy process and some very light Hölder-continuity assumptions on the drift and diffusion coefficients. © 2013 Elsevier Inc. All rights reserved.