Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929674595074048 |
|---|---|
| author | Bayraktar, Erhan Ekren, Ibrahim Zhang, Xin |
| author_facet | Bayraktar, Erhan Ekren, Ibrahim Zhang, Xin |
| contents | In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dimensional inf(sup)-convolution of the finite-dimensional value function yields a super (sub)-viscosity solution to the PDEs on Wasserstein space. Hence, we obtain a convergence rate using a comparison principle of such PDEs on Wasserstein space. Our argument is purely analytic and relies on the regularity of value functions established in \cite{DaJaSe23}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06013 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space Bayraktar, Erhan Ekren, Ibrahim Zhang, Xin Analysis of PDEs 49L25, 60H30, 93E20 In this paper, we provide a convergence rate for particle approximations of a class of second-order PDEs on Wasserstein space. We show that, up to some error term, the infinite-dimensional inf(sup)-convolution of the finite-dimensional value function yields a super (sub)-viscosity solution to the PDEs on Wasserstein space. Hence, we obtain a convergence rate using a comparison principle of such PDEs on Wasserstein space. Our argument is purely analytic and relies on the regularity of value functions established in \cite{DaJaSe23}. |
| title | Convergence Rate of Particle System for Second-order PDEs On Wasserstein Space |
| topic | Analysis of PDEs 49L25, 60H30, 93E20 |
| url | https://arxiv.org/abs/2408.06013 |