A coupling strategy for Brownian motions at fixed time on Carnot groups using Legendre expansion
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910514832998400 |
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| author | Arnaudon, Marc Bénéfice, Magalie Bonnefont, Michel Féral, Delphine |
| author_facet | Arnaudon, Marc Bénéfice, Magalie Bonnefont, Michel Féral, Delphine |
| contents | We propose a new simple construction of a coupling at a fixed time of two sub-Riemannian Brownian motions on the Heisenberg group and on the free step 2 Carnot groups. The construction is based on a Legendre expansion of the standard Brownian motion and of the L{é}vy area. We deduce sharp estimates for the decay in total variation distance between the laws of the Brownian motions. Using a change of probability method, we also obtain the log-Harnack inequality, a Bismut type integration by part formula and reverse Poincaré inequalities for the associated semi-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04321 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A coupling strategy for Brownian motions at fixed time on Carnot groups using Legendre expansion Arnaudon, Marc Bénéfice, Magalie Bonnefont, Michel Féral, Delphine Probability We propose a new simple construction of a coupling at a fixed time of two sub-Riemannian Brownian motions on the Heisenberg group and on the free step 2 Carnot groups. The construction is based on a Legendre expansion of the standard Brownian motion and of the L{é}vy area. We deduce sharp estimates for the decay in total variation distance between the laws of the Brownian motions. Using a change of probability method, we also obtain the log-Harnack inequality, a Bismut type integration by part formula and reverse Poincaré inequalities for the associated semi-group. |
| title | A coupling strategy for Brownian motions at fixed time on Carnot groups using Legendre expansion |
| topic | Probability |
| url | https://arxiv.org/abs/2407.04321 |