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- Title
The Malliavin calculus and hypoelliptic differential operators.
- Authors
Bell, Denis
- Abstract
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.
- Subjects
MALLIAVIN calculus; HYPOELLIPTIC operators; ELLIPTIC operators; STOCHASTIC analysis; MATHEMATICAL proofs
- Publication
Infinite Dimensional Analysis, Quantum Probability & Related Topics, 2015, Vol 18, Issue 1, p-1
- ISSN
0219-0257
- Publication type
Article
- DOI
10.1142/S0219025715500010