An exercise in Malliavin’s calculus. (English) Zbl 1329.35121

Summary: 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.


35H10 Hypoelliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
60J65 Brownian motion
60H07 Stochastic calculus of variations and the Malliavin calculus
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