Ornstein-Uhlenbeck Type Processes on Wasserstein Space
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866910366272847872 |
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| author | Ren, Panpan Wang, Feng-Yu |
| author_facet | Ren, Panpan Wang, Feng-Yu |
| contents | Let $\mathcal P_2$ be the space of probability measures on $\R^d$ having finite second moment, and consider the Riemannian structure on $\mathcal P_2$ induced by the intrinsic derivative on the $L^2$-tangent space. By using stochastic analysis on the tangent space, we construct an Ornstein$-$Uhlenbeck (OU) type Dirichlet form on $\mathcal P_2$ whose generator is formally given by the intrinsic Laplacian with a drift. The log-Sobolev inequality holds and the associated Markov semigroup is $L^2$-compact.
Perturbations of the OU Dirichlet form are also studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_05479 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Ornstein-Uhlenbeck Type Processes on Wasserstein Space Ren, Panpan Wang, Feng-Yu Probability Let $\mathcal P_2$ be the space of probability measures on $\R^d$ having finite second moment, and consider the Riemannian structure on $\mathcal P_2$ induced by the intrinsic derivative on the $L^2$-tangent space. By using stochastic analysis on the tangent space, we construct an Ornstein$-$Uhlenbeck (OU) type Dirichlet form on $\mathcal P_2$ whose generator is formally given by the intrinsic Laplacian with a drift. The log-Sobolev inequality holds and the associated Markov semigroup is $L^2$-compact. Perturbations of the OU Dirichlet form are also studied. |
| title | Ornstein-Uhlenbeck Type Processes on Wasserstein Space |
| topic | Probability |
| url | https://arxiv.org/abs/2206.05479 |