Adapted Wasserstein distance between the laws of SDEs
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866916998735200256 |
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| author | Backhoff-Veraguas, Julio Källblad, Sigrid Robinson, Benjamin A. |
| author_facet | Backhoff-Veraguas, Julio Källblad, Sigrid Robinson, Benjamin A. |
| contents | We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes. We complement our main results with examples showing how the optimal coupling may change in path-dependent and multidimensional settings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_03243 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Adapted Wasserstein distance between the laws of SDEs Backhoff-Veraguas, Julio Källblad, Sigrid Robinson, Benjamin A. Probability 60H10, 49Q22 (Primary), 60H35, 93E20 (Secondary) We consider the bicausal optimal transport problem between the laws of scalar time-homogeneous stochastic differential equations, and we establish the optimality of the synchronous coupling between these laws. The proof of this result is based on time-discretisation and reveals a novel connection between the synchronous coupling and the celebrated discrete-time Knothe--Rosenblatt rearrangement. We also prove a result on equality of topologies restricted to a certain subset of laws of continuous-time processes. We complement our main results with examples showing how the optimal coupling may change in path-dependent and multidimensional settings. |
| title | Adapted Wasserstein distance between the laws of SDEs |
| topic | Probability 60H10, 49Q22 (Primary), 60H35, 93E20 (Secondary) |
| url | https://arxiv.org/abs/2209.03243 |