| Issue |
ESAIM: PS
Volume 29, 2025
|
|
|---|---|---|
| Page(s) | 324 - 356 | |
| DOI | https://doi.org/10.1051/ps/2025006 | |
| Published online | 18 July 2025 | |
Non co-adapted couplings of Brownian motions on free, step 2 Carnot groups
Université de Lorraine, CNRS, IECL, F-54000 Nancy, France.
* Corresponding author: magalie.benefice@univ-lorraine.fr
Received:
16
July
2024
Accepted:
28
March
2025
On the free, step 2 Carnot groups of rank n 𝔾n, the subRiemannian Brownian motion consists in a ℝn -Brownian motion together with its n(n−1)/2 Lévy areas. In this article we construct an explicit successful non co-adapted coupling of Brownian motions on 𝔾n. We use this construction to obtain gradient inequalities for the heat semi-group on all the homogeneous step 2 Carnot groups. Comparing the first coupling time and the first exit time from a domain, we also obtain gradient inequalities for harmonic functions on 𝔾n. These results generalize the coupling strategy by Banerjee, Gordina and Mariano on the Heisenberg group.
Mathematics Subject Classification: 58J65 / 60B15 / 60J60 / 60H30
Key words: Non Markovian coupling / successful coupling / Carnot groups / Brownian motion / Lévy area
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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