The Malliavin calculus and hypoelliptic differential operators

Document Type

Article

Publication Date

3-25-2015

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.

Publication Title

Infinite Dimensional Analysis, Quantum Probability and Related Topics

Volume

18

Issue

1

Digital Object Identifier (DOI)

10.1142/S0219025715500010

ISSN

02190257

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