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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.13634 |
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| _version_ | 1866909650185617408 |
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| author | Acciaio, Beatrice Kršek, Daniel Pammer, Gudmund Rodrigues, Marco |
| author_facet | Acciaio, Beatrice Kršek, Daniel Pammer, Gudmund Rodrigues, Marco |
| contents | We study absolutely continuous curves in the adapted Wasserstein space of filtered processes. We provide a probabilistic representation of such curves as flows of adapted processes on a common filtered probability space, extending classical results to the adapted setting. Moreover, we characterize geodesics in this space and derive an adapted Benamou--Brenier-type formula by reformulating adapted optimal transport as an energy minimization problem. As an application, we obtain a Skorokhod-type representation for sequences of filtered processes under the adapted weak topology. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absolutely Continuous Curves of Stochastic Processes Acciaio, Beatrice Kršek, Daniel Pammer, Gudmund Rodrigues, Marco Probability We study absolutely continuous curves in the adapted Wasserstein space of filtered processes. We provide a probabilistic representation of such curves as flows of adapted processes on a common filtered probability space, extending classical results to the adapted setting. Moreover, we characterize geodesics in this space and derive an adapted Benamou--Brenier-type formula by reformulating adapted optimal transport as an energy minimization problem. As an application, we obtain a Skorokhod-type representation for sequences of filtered processes under the adapted weak topology. |
| title | Absolutely Continuous Curves of Stochastic Processes |
| topic | Probability |
| url | https://arxiv.org/abs/2506.13634 |