{"paper":{"title":"Diffusion Processes on $p$-Wasserstein Space over Banach Space","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Feng-Yu Wang, Panpan Ren, Simon Wittmann","submitted_at":"2024-02-23T06:32:01Z","abstract_excerpt":"To study diffusion processes on the p-Wasserstein space $\\mathscr P_p$ for $p\\in [1,\\infty)$ over a separable, reflexive Banach space $X$, we present a criterion on the quasi-regularity of Dirichlet forms in $L^2(\\mathscr P_p,\\Lambda)$ for a reference probability $\\Lambda$ on $\\mathscr P_p$. It is formulated in terms of an upper bound condition with the uniform norm of the intrinsic derivative. We find a versatile class of quasi-regular local Dirichlet forms on $\\mathscr P_p$ by using images of Dirichlet forms on the tangent space $L^p(X\\to X,\\mu_0)$ at a reference point $\\mu_0\\in\\mathscr P_p$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.15130","kind":"arxiv","version":4},"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/2402.15130/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"}