{"paper":{"title":"The Wasserstein space of stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Daniel Bartl, Gudmund Pammer, Mathias Beiglb\\\"ock","submitted_at":"2021-04-29T10:26:31Z","abstract_excerpt":"Wasserstein distance induces a natural Riemannian structure for the probabilities on the Euclidean space. This insight of classical transport theory is fundamental for tremendous applications in various fields of pure and applied mathematics. We believe that an appropriate probabilistic variant, the adapted Wasserstein distance AW, can play a similar role for the class FP of filtered processes, i.e. stochastic processes together with a filtration. In contrast to other topologies for stochastic processes, probabilistic operations such as the Doob-decomposition, optimal stopping and stochastic c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.14245","kind":"arxiv","version":2},"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/2104.14245/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"}