{"paper":{"title":"Lower path regularity in all dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonas M. T\\\"olle, Lauri Viitasaari, Michael Hinz","submitted_at":"2026-05-26T21:38:18Z","abstract_excerpt":"We prove precise almost sure lower path regularity results for a wide class of stochastic processes in all space dimensions $d\\geq 1$. Examples include Gaussian processes, in particular, fractional Brownian motions with Hurst index $H\\in (0,1)$, Rosenblatt processes, and solutions to stochastic differential equations driven by fractional Brownian motions with Hurst index $H\\in (\\frac{1}{4},1)$, all in arbitrary dimensions $d\\ge 1$. Our key tool is a new continuity result for Riesz potentials of occupation measures, which we use as substitutes for local times."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27713","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/2605.27713/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"}