Stochastic completeness and gradient representations for sub-Riemannian manifolds

Grong, Erlend; Thalmaier, Anton

doi:10.1007/s11118-018-9710-x

Reference : Stochastic completeness and gradient representations for sub-Riemannian manifolds


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/29398

Title :	Stochastic completeness and gradient representations for sub-Riemannian manifolds
Language :	English
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 >]
Publication date :	Aug-2019
Journal title :	Potential Analysis
Publisher :	Springer
Volume :	51
Issue/season :	2
Pages :	219-254
Peer reviewed :	Yes
Audience :	International
ISSN :	0926-2601
e-ISSN :	1572-929X
City :	Amsterdam
Country :	The Netherlands
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.
Funders :	University of Luxembourg - UL
Name of the research project :	R-AGR-0517 > AGSDE > 01/09/2015 - 31/08/2018 > THALMAIER Anton
Target :	Researchers ; Professionals
Permalink :	http://hdl.handle.net/10993/29398
DOI :	10.1007/s11118-018-9710-x
Other URL :	http://arxiv.org/abs/1605.00785
FnR project :	FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

File(s) associated to this reference

Fulltext file(s):

	File	Commentary	Version	Size	Access
Open access	GTSCompleteSR1-1.pdf		Author preprint	522.93 kB	View/Open

All documents in ORBi^lu are protected by a user license.

University of Luxembourg Library | Feedback | Legal notices