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Geometry of subelliptic diffusions
Thalmaier, Anton
2016In Barilari, Davide; Boscain, Ugo; Sigalotti, Mario (Eds.) Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II
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Abstract :
[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 :
Mathematics
Author, co-author :
Thalmaier, Anton ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
no
Language :
English
Title :
Geometry of subelliptic diffusions
Publication date :
2016
Main work title :
Geometry, Analysis and Dynamics on sub-Riemannian Manifolds. Volume II
Editor :
Barilari, Davide
Boscain, Ugo
Sigalotti, Mario
Publisher :
EMS Publishing House, Zürich, Switzerland
ISBN/EAN :
978-3-03719-163-7
Collection name :
EMS Series of Lectures in Mathematics (ELM)
Pages :
85-169
Peer reviewed :
Peer reviewed
FnR Project :
FNR7628746 - Geometry Of Random Evolutions, 2014 (01/03/2015-28/02/2018) - Anton Thalmaier
Name of the research project :
R-AGR-0517 - IRP15 - AGSDE (20150901-20190630) - THALMAIER Anton
Commentary :
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).
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