{"paper":{"title":"On Multidimensional stable-driven Stochastic Differential Equations with Besov drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"HSE), Paul-Eric Chaudru de Raynal (LMJL), St\\'ephane Menozzi (LaMME","submitted_at":"2019-07-29T08:20:08Z","abstract_excerpt":"We establish well-posedness results for multidimensional non degenerate $\\alpha$-stable driven SDEs with time inhomogeneous singular drifts in $\\mathbb{L}^r-{\\mathbb B}_{p,q}^{-1+\\gamma}$ with $\\gamma<1$ and $\\alpha$ in $(1,2]$, where $\\mathbb{L}^r$ and ${\\mathbb B}_{p,q}^{-1+\\gamma} $ stand for Lebesgue and Besov spaces respectively. Precisely, we first prove the well-posedness of the corresponding martingale problem and then give a precise meaning to the dynamics of the SDE. This allows us in turn to define an ad hoc notion of weak solution, for which well-posedness holds as well. Our result"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.12263","kind":"arxiv","version":3},"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/1907.12263/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"}