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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.

MSC:

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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References:

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