"Malliavin’s work inspired many new results in stochastic analysis. Examples include filtering theorems (Michel ...), a deeper understanding of the Skorohod integral and the development of an anticipating stochastic calculus (Nualart and Paradox ...), an extension of Clark’s formula (Ocone ...), Bismut’s probabilistic analysis of the small-time asymptotics of the heat kernel of the Dirac operator on a Riemannian manifold ... and his subsequent proof of the associated index theorem ..., and a sharp hypoellipticity theorem for Hörmander operators with hypersurfaces of infinite type (Bell and Mohammed ...)."