Existence of densities for stable-like driven SDE's with H?lder continuous coefficients

摘要

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 non-degeneracy condition on the driving Lévy process and some very light H?lder-continuity assumptions on the drift and diffusion coefficients.