[en] The lectures focus on some probabilistic aspects related to sub-Riemannian geometry. The main intention is to give an introduction to hypoelliptic and subelliptic diffusions. The notes are written from a geometric point of view trying to minimize the weight of ``probabilistic baggage'' necessary to follow the arguments. We discuss in particular the following topics: stochastic flows to second order differential operators; smoothness of transition probabilities under Hörmander's brackets condition; control theory and Stroock-Varadhan's support theorems; Malliavin calculus; Hörmander's theorem. The notes start from well-known facts in Geometric Stochastic Analysis and guide to recent on-going
research topics, like hypoelliptic heat kernel estimates; gradient
estimates and Harnack type inequalities for subelliptic diffusion
semigroups; notions of curvature related to sub-Riemannian
diffusions.
Disciplines :
Mathématiques
Auteur, co-auteur :
THALMAIER, Anton ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Geometry of subelliptic diffusions
Date de publication/diffusion :
2016
Titre de l'ouvrage principal :
Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
Intitulé du projet de recherche :
R-AGR-0517 - IRP15 - AGSDE (20150901-20190630) - THALMAIER Anton
Commentaire :
These are notes to a series of lectures given at the CIRM Summer School on "Sub-Riemannian manifolds: from geodesics to hypoelliptic diffusions"which took place at the Centre International de Rencontres Mathématiques in Marseille, as part of the IHP Trimester program "Geometry, Analysis and Dynamics on Sub-Riemannian manifolds" (Institut Henri Poincaré in Paris from Sept. 1 to Dec. 14, 2014).
