Reference : Stochastic completeness and gradient representations for sub-Riemannian manifolds
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Stochastic completeness and gradient representations for sub-Riemannian manifolds
Grong, Erlend [Université Paris-Sud 11 > Laboratoire des Signaux et Système]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Potential Analysis
Yes (verified by ORBilu)
The Netherlands
[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.
University of Luxembourg - UL
Researchers ; Professionals
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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