Non-Gaussian Malliavin Calculus on Real Lie Algebras
Abstract
The non-commutative Malliavin calculus on the Heisenberg-Weyl algebra is extended to the affine algebra. A differential calculus and a non-commutative integration by parts are established. As an application we obtain sufficient conditions for the smoothness of Wignertypelaws of non-commutativerandom variables with gamma or continuous binomial marginals.