Couplings in $L^p$ distance of two Brownian motions and their Lévy area
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BONNEFONT, Michel | |
| hal.structure.identifier | Institut de Recherche Mathématique Avancée [IRMA] | |
| dc.contributor.author | JUILLET, Nicolas | |
| dc.date.accessioned | 2024-04-04T03:01:56Z | |
| dc.date.available | 2024-04-04T03:01:56Z | |
| dc.date.issued | 2020 | |
| dc.identifier.issn | 0246-0203 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/192935 | |
| dc.description.abstractEn | We study co-adapted couplings of (canonical hypoelliptic) diffu-sions on the (subRiemannian) Heisenberg group, that we call (Heisenberg) Brow-nian motions and are the joint laws of a planar Brownian motion with its Lévy area. We show that contrary to the situation observed on Riemannian manifolds of non-negative Ricci curvature, for any co-adapted coupling, two Heisenberg Brownian motions starting at two given points can not stay at bounded distance for all time t ≥ 0. Actually, we prove the stronger result that they can not stay bounded in L p for p ≥ 2. We also study the coupling by reflection, and show that it stays bounded in L p for 0 ≤ p < 1. Finally, we explain how the results generalise to the Heisenberg groups of higher dimension | |
| dc.language.iso | en | |
| dc.publisher | Institut Henri Poincaré (IHP) | |
| dc.title.en | Couplings in $L^p$ distance of two Brownian motions and their Lévy area | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1214/19-AIHP972 | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 1801.04109 | |
| bordeaux.journal | Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01671676 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01671676v1 | |
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