This note has two goals. First, for those who have heard the term but do not know what it means, it provides a gentle introduction to Malliavin's calculus as it applies to degenerate parabolic partial differential equations. Second, it applies that theory to generalizations of Kolmogorov's example of a highly degenerate operator which is nonetheless hypoelliptic.
"An exercise in Malliavin's calculus." J. Math. Soc. Japan 67 (4) 1785 - 1799, October, 2015. https://doi.org/10.2969/jmsj/06741785