Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Université de Bordeaux [UB] | |
| dc.contributor.author | BÉNÉFICE, Magalie | |
| dc.date.accessioned | 2024-04-04T02:29:32Z | |
| dc.date.available | 2024-04-04T02:29:32Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190183 | |
| dc.description.abstractEn | 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 $SL(2,\mathbb{R})$. | |
| dc.language.iso | en | |
| dc.subject.en | SubRiemannian manifolds | |
| dc.subject.en | Brownian motion | |
| dc.subject.en | Coupling | |
| dc.subject.en | Co-adapted coupling | |
| dc.subject.en | Successful coupling | |
| dc.title.en | Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$ | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Probabilités [math.PR] | |
| dc.identifier.arxiv | 2305.10017 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04099288 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04099288v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=B%C3%89N%C3%89FICE,%20Magalie&rft.genre=preprint |
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