Pré-Publication, Document De Travail Année : 2024

Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$

Résumé

The Lie groups $SU(2)$ and $SL(2,\mathbb{R})$ can be viewed as model spaces in subRiemannian geometry. Coupling two subelliptic Brownian motions on $SU(2)$ (resp. $SL(2,\mathbb{R})$) consists in coupling two Brownian motions on the sphere (resp. the hyperbolic plane) and simultaneously their swept areas. Using this approach we propose an explicit construction of a co-adapted successful coupling on $SU(2)$. The strategy is to alternate between reflection and synchronous (with noise) coupling on the sphere. We also describe some more general constructions of co-adapted couplings on $SU(2)$ and also on $SL(2,\mathbb{R})$.

Fichier principal
Vignette du fichier
VSHAl-V3.pdf (452.93 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Licence

Dates et versions

hal-04099288 , version 1 (16-05-2023)
hal-04099288 , version 2 (22-12-2023)
hal-04099288 , version 3 (30-03-2024)

Licence

Identifiants

Citer

Magalie Bénéfice. Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$. 2024. ⟨hal-04099288v3⟩
99 Consultations
415 Téléchargements

Altmetric

Partager

  • More