Reference : Functional inequalities on path space of sub-Riemannian manifolds and applications
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/41284
Functional inequalities on path space of sub-Riemannian manifolds and applications
English
Cheng, Li Juan [Department of Applied Mathematics > Zhejiang University of Technology, Hangzhou]
Grong, Erlend [University of Bergen > Department of Mathematics]
Thalmaier, Anton mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Sep-2021
Nonlinear Analysis: Theory, Methods and Applications
Elsevier
210
112387
1-30
Yes
International
0362-546X
Oxford
UK
[en] We consider the path space of a manifold with a measure induced by a stochastic flow with an infinitesimal generator that is hypoelliptic, but not elliptic. These generators can be seen as sub-Laplacians of a sub-Riemannian structure with a chosen complement. We introduce a concept of gradient for cylindrical functionals on path space in such a way that the gradient operators are closable in L^2. With this structure in place, we show that a bound on horizontal Ricci curvature is equivalent to several inequalities for functions on path space, such as a gradient inequality, log-Sobolev inequality and Poincaré inequality. As a consequence, we also obtain a bound for the spectral gap of the Ornstein-Uhlenbeck operator.
R-AGR-0517 > AGSDE > 01/09/2015 - 31/08/2018 > THALMAIER Anton
Researchers
http://hdl.handle.net/10993/41284
10.1016/j.na.2021.112387
https://authors.elsevier.com/sd/article/S0362546X21000924
FnR ; FNR7628746 > Anton Thalmaier > GEOMREV > Geometry of random evolutions > 01/03/2015 > 28/02/2018 > 2014

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