Smoothness of the law of manifold-valued Markov processes with jumps

Abstract

Consider on a manifold the solution $X$ of a stochastic differential equation driven by a Lévy process without Brownian part. Sufficient conditions for the smoothness of the law of $X_t$ are given, with particular emphasis on noncompact manifolds. The result is deduced from the case of affine spaces by means of a localisation technique. The particular cases of Lie groups and homogeneous spaces are discussed.