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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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Table of 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.