Article (Scientific journals)
Radial processes for sub-Riemannian Brownian motions and applications
Baudoin, Fabrice; Grong, Erlend; Kuwada, Kazumasa et al.
2020In Electronic Journal of Probability, 25 (paper no. 97), p. 1-17
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Abstract :
[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.
Disciplines :
Author, co-author :
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 ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
Language :
Title :
Radial processes for sub-Riemannian Brownian motions and applications
Publication date :
13 August 2020
Journal title :
Electronic Journal of Probability
Publisher :
Institute of Mathematical Statistics, Beachwood, United States - Ohio
Volume :
Issue :
paper no. 97
Pages :
Peer reviewed :
Peer Reviewed verified by ORBi
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
Funders :
University of Luxembourg - UL
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