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

Jean Picard (1) , Catherine Savona (1)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal

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.

Mots clés: Malliavin calculus; processes with jumps; manifold-valued processes; Lie groups and homogeneous spaces.; Lie groups and homogeneous spaces

Domaines: Probabilités [math.PR]

Jean Picard, Catherine Savona. Smoothness of the law of manifold-valued Markov processes with jumps. Bernoulli, 2013, 19 (5A), pp.1880-1919. ⟨10.3150/12-BEJ434⟩. ⟨hal-00602692v2⟩