{"paper":{"title":"On weak solutions of stochastic differential equations with sharp drift coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Guangying Lv, Jiang-Lun Wu, Jinlong Wei","submitted_at":"2017-11-14T11:11:03Z","abstract_excerpt":"We extend Krylov and R\\\"{o}ckner's result \\cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs. To be more precise, let $b: [0,T]\\times{\\mathbb R}^d\\rightarrow{\\mathbb R}^d$ be Borel measurable, where $T>0$ is arbitrarily fixed. Consider $$X_t=x+\\int_0^tb(s,X_s)ds+W_t,\\quad t\\in[0,T], \\, x\\in{\\mathbb R}^d,$$ where $\\{W_t\\}_{t\\in[0,T]}$ is a $d$-dimensional standard Wiener process. If $b=b_1+b_2$ such that $b_1(T-\\cdot)\\in\\mathcal{C}_q^0((0,T];L^p({\\mathbb R}^d))$ with $2/q+d/p=1$ for $p,q\\ge1$ and $\\|b_1(T-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05058","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":""},"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"}