Malliavin Calculus and Stochastic Analysis on Manifolds

Malliavin calculus is an abstract infinite dimensional calculus on abstract Gaussian probability spaces. Combined with corresponding probabilistic representations it can be an extremely useful tool in the analysis of PDE problems of which the Hörmander theorem for hypoelliptic operators is a celebrated example. In the second part of the lecture we will extend this to the case of Riemannian manifolds where we discuss probabilistic methods for the derivation of heat kernel bounds and the prominent role of Ricci curvature.

Date and time info
Monday 15:00 - 17:00

Keywords
Probability Theory & Elements of Ito Stochastic Calculus, Elements of Differential Geometry

Audience
MSc students, PhD students, Postdocs

Language
English