{"paper":{"title":"Pathwise Uniqueness for Multiplicative Young and Rough Differential Equations Driven by Fractional Brownian Motion","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Avi Mayorcas, Toyomu Matsuda","submitted_at":"2023-12-11T16:01:11Z","abstract_excerpt":"We show pathwise uniqueness of multiplicative SDEs, in arbitrary dimensions, driven by fractional Brownian motion with Hurst parameter $H\\in (1/3,1)$ with volatility coefficient $\\sigma$ that is at least $\\gamma$-H\\\"older continuous for $\\gamma > \\frac{1}{2H} \\vee \\frac{1-H}{H}$. This improves upon the long-standing results of [Lyo94 , Lyo98 , Dav08] which cover the same regime but require $\\sigma$ to be at least $\\frac{1}{H}$-H\\\"older continuous. Our central innovation is to combine stochastic averaging estimates with refined versions of the stochastic sewing lemma, due to [L\\^e20, Ger22, MP2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.06473","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/2312.06473/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"}