{"paper":{"title":"Absolutely Continuous Curves of Stochastic Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Beatrice Acciaio, Daniel Kr\\v{s}ek, Gudmund Pammer, Marco Rodrigues","submitted_at":"2025-06-16T16:00:21Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.13634","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.13634/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}