Existence and smoothness of transition density for jump-type Markov processes: Applications of Malliavin calculus (Q1198468)

Consider a pure jump diffusion process of a type, called stable-like process by Bass, and which is a generalization of Lévy stable processes. One looks for conditions ensuring the existence and the smoothness of a density for the transition probability. This work contains sufficient conditions for this problem. A differential calculus is constructed on a Poisson space, and a Malliavin calculus is developed in order to prove the results.