Reference : Radial processes for sub-Riemannian Brownian motions and applications
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/42457
Radial processes for sub-Riemannian Brownian motions and applications
English
Baudoin, Fabrice [University of Connecticut - UCONN > Department of Mathematics]
Grong, Erlend [University of Bergen > Department of Mathematics]
Kuwada, Kazumasa [Tohoku University > Department of Mathematics]
Neel, Robert [Lehigh University > Department of Mathematics]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
10-Feb-2020
21
No
[en] We study the radial part of sub-Riemannian Brownian motion in the context of totally geodesic foliations. Itô's formula is proved for the radial processes associated to Riemannian distances approximating the Riemannian one. We deduce very general stochastic completeness criteria for the sub-Riemannian Brownian motion. In the context of Sasakian foliations and H-type groups, one can push the analysis further, and taking advantage of the recently proved sub-Laplacian comparison theorems one can compare the radial processes for the sub-Riemannian distance to one-dimensional model diffusions. As a geometric application, we prove Cheng's type estimates for the Dirichlet eigenvalues of the sub-Riemannian metric balls, a result which seems to be new even in the Heisenberg group.
University of Luxembourg - UL
R-AGR-0517 > AGSDE > 01/09/2015 - 31/08/2018 > THALMAIER Anton
Researchers
http://hdl.handle.net/10993/42457
https://arxiv.org/abs/2002.02556
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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