On gradient bounds for the heat kernel on the Heisenberg group, Journal of Functional Analysis, vol.255, issue.8, pp.1905-1938, 2008. ,
DOI : 10.1016/j.jfa.2008.09.002
URL : https://hal.archives-ouvertes.fr/hal-00179865
Coupling in the Heisenberg group and its applications to gradient estimates. ArXiv e-prints, 2016. ,
Curvature-dimension inequalities and Ricci lower bounds for sub-Riemannian manifolds with transverse symmetries, Journal of the European Mathematical Society, vol.19, issue.1, pp.151-219, 2017. ,
DOI : 10.4171/JEMS/663
Coupling constructions for hypoelliptic diffusions: two examples, In Stochastic analysis Proc. Sympos. Pure Math, vol.57, pp.193-212, 1993. ,
DOI : 10.1090/pspum/057/1335472
Handbook of Brownian motion?facts and formulae. Probability and its Applications, 2002. ,
Gradient estimates on manifolds using coupling, Journal of Functional Analysis, vol.99, issue.1, pp.110-124, 1991. ,
DOI : 10.1016/0022-1236(91)90054-9
URL : https://doi.org/10.1016/0022-1236(91)90054-9
A probabilistic approach to gradient estimates, Bulletin canadien de math??matiques, vol.35, issue.1, pp.46-55, 1992. ,
DOI : 10.4153/CMB-1992-007-6
Hypoelliptic heat kernel inequalities on the Heisenberg group, Journal of Functional Analysis, vol.221, issue.2, pp.340-365, 2005. ,
DOI : 10.1016/j.jfa.2004.06.012
URL : https://doi.org/10.1016/j.jfa.2004.06.012
Maximal Coupling of Euclidean Brownian Motions, Communications in Mathematics and Statistics, vol.11, issue.3, pp.93-104, 2013. ,
DOI : 10.1090/gsm/058
Geometric Inequalities and Generalized Ricci Bounds in the Heisenberg Group, International Mathematics Research Notices, 2009. ,
DOI : 10.1093/imrn/rnp019
Coupling all the L??vy stochastic areas of multidimensional Brownian motion, The Annals of Probability, vol.35, issue.3, pp.935-953, 2007. ,
DOI : 10.1214/009117906000001196
Brownian couplings, convexity, and shy-ness, Electronic Communications in Probability, vol.14, issue.0, pp.66-80, 2009. ,
DOI : 10.1214/ECP.v14-1417
URL : http://arxiv.org/pdf/0809.4682
Coupling time distribution asymptotics for some couplings of the L??vy stochastic area, Probability and mathematical genetics, pp.446-463, 2010. ,
DOI : 10.1017/CBO9781139107174.021
On Uniqueness of Maximal Coupling for Diffusion??Processes with a Reflection, Journal of Theoretical Probability, vol.9, issue.14, pp.935-957, 2007. ,
DOI : 10.1214/EJP.v9-205
Duality on gradient estimates and Wasserstein controls, Journal of Functional Analysis, vol.258, issue.11, pp.3758-3774, 2010. ,
DOI : 10.1016/j.jfa.2010.01.010
URL : https://doi.org/10.1016/j.jfa.2010.01.010
A counterexample for the optimality of Kendall-Cranston coupling, Electronic Communications in Probability, vol.12, issue.0, pp.66-72, 2007. ,
DOI : 10.1214/ECP.v12-1160
Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg, Journal of Functional Analysis, vol.236, issue.2, pp.369-394, 2006. ,
DOI : 10.1016/j.jfa.2006.02.016
URL : https://doi.org/10.1016/j.jfa.2006.02.016
A Tour of Subriemannian Geometries, Their Geodesics and Applications, volume 91 of Mathematical Surveys and Monographs, 2002. ,
Shy and fixed-distance couplings of Brownian motions on manifolds, Stochastic Processes and their Applications, vol.126, issue.2, pp.628-650, 2016. ,
DOI : 10.1016/j.spa.2015.09.014
URL : http://arxiv.org/pdf/1210.7217
Continuous martingales and Brownian motion, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1999. ,
Intrinsic Coupling on Riemannian Manifolds and Polyhedra, Electronic Journal of Probability, vol.9, issue.0, pp.411-435, 2004. ,
DOI : 10.1214/EJP.v9-205
Transport inequalities, gradient estimates, entropy and Ricci curvature, Communications on Pure and Applied Mathematics, vol.108, issue.7, pp.923-940, 2005. ,
DOI : 10.1090/gsm/058
On estimation of the logarithmic Sobolev constant and gradient estimates of heat semigroups. Probab. Theory Related Fields, pp.87-101, 1997. ,