Simulation of infinite-dimensional diffusion bridges
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866929762238201856 |
|---|---|
| author | Pieper-Sethmacher, Thorben van der Meulen, Frank van der Vaart, Aad |
| author_facet | Pieper-Sethmacher, Thorben van der Meulen, Frank van der Vaart, Aad |
| contents | Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation LXT of the final state XT at some time T > 0. This solves a problem that has so far not been attended to in the literature. Our main contribution is the derivation of a path measure that is absolutely continuous with respect to the path measure of the infinite-dimensional diffusion bridge. This lifts previously known results for stochastic ordinary differential equations to the setting of infinite-dimensional diffusions and stochastic partial differential equations. We demonstrate our findings through numerical experiments on stochastic reaction-diffusion equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13177 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Simulation of infinite-dimensional diffusion bridges Pieper-Sethmacher, Thorben van der Meulen, Frank van der Vaart, Aad Probability Let X be the mild solution to a semilinear stochastic partial differential equation. In this article, we develop methodology to sample from the infinite-dimensional diffusion bridge that arises from conditioning X on a linear transformation LXT of the final state XT at some time T > 0. This solves a problem that has so far not been attended to in the literature. Our main contribution is the derivation of a path measure that is absolutely continuous with respect to the path measure of the infinite-dimensional diffusion bridge. This lifts previously known results for stochastic ordinary differential equations to the setting of infinite-dimensional diffusions and stochastic partial differential equations. We demonstrate our findings through numerical experiments on stochastic reaction-diffusion equations. |
| title | Simulation of infinite-dimensional diffusion bridges |
| topic | Probability |
| url | https://arxiv.org/abs/2503.13177 |