Article (Scientific journals)
Stochastic completeness and gradient representations for sub-Riemannian manifolds
Grong, Erlend; THALMAIER, Anton
2019In Potential Analysis, 51 (2), p. 219-254
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Abstract :
[en] Given a second order partial differential operator L satisfying the strong Hörmander condition with corresponding heat semigroup P_t, we give two different stochastic representations of dP_t f for a bounded smooth function f. We show that the first identity can be used to prove infinite lifetime of a diffusion of L/2, while the second one is used to find an explicit pointwise bound for the horizontal gradient on a Carnot group. In both cases, the underlying idea is to consider the interplay between sub-Riemannian geometry and connections compatible with this geometry.
Disciplines :
Mathematics
Author, co-author :
Grong, Erlend;  Université Paris-Sud 11 > Laboratoire des Signaux et Système
THALMAIER, Anton ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
Stochastic completeness and gradient representations for sub-Riemannian manifolds
Publication date :
August 2019
Journal title :
Potential Analysis
ISSN :
1572-929X
Publisher :
Springer, Amsterdam, Netherlands
Volume :
51
Issue :
2
Pages :
219-254
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
Available on ORBilu :
since 16 January 2017

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