The Malliavin calculus and hypoelliptic differential operators
This article is intended as an introduction to Malliavin's stochastic calculus of variations and his probabilistic approach to hypoellipticity. Topics covered include an elementary derivation of the basic integration by parts formulae, a proof of the probabilistic version of Hörmander's theorem as envisioned by Malliavin and completed by Kusuoka and Stroock, and an extension of Hörmander's theorem valid for operators with degeneracy of exponential type due to the author and S. Mohammed.
Infinite Dimensional Analysis, Quantum Probability and Related Topics
Digital Object Identifier (DOI)
Bell. (2015). The Malliavin calculus and hypoelliptic differential operators. Infinite Dimensional Analysis, Quantum Probability, and Related Topics, 18(1), 1550001–. https://doi.org/10.1142/S0219025715500010