Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Accesso online: | |
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| _version_ | 1866909156373430272 |
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| author | Bénéfice, Magalie |
| author_facet | Bénéfice, Magalie |
| contents | 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 $SL(2,\mathbb{R})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$ Bénéfice, Magalie Probability 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 $SL(2,\mathbb{R})$. |
| title | Couplings of Brownian motions on $SU(2,\mathbb{C})$ and $SL(2,\mathbb{R})$ |
| topic | Probability |
| url | https://arxiv.org/abs/2305.10017 |