{"paper":{"title":"Flows for Singular Stochastic Differential Equations with Unbounded Drifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Olivier Menoukeu Pamen, Salah E. A. Mohammed","submitted_at":"2017-04-12T10:01:11Z","abstract_excerpt":"In this paper, we are interested in the following singular stochastic differential equation (SDE) $${\\rm d} X_t = b(t,X_t) {\\rm d}  t + {\\rm d}  B_{t},\\ 0\\leq t\\leq T,\\ X_0 = x \\in \\mathbb{R}^d,$$ where the drift coefficient $b:[0,T]\\times \\mathbb{R}^{d}\\longrightarrow \\mathbb{R}^{d}$ is Borel measurable, possibly unbounded and has spatial linear growth. The driving noise $B_{t}$ is a $d-$ dimensional Brownian motion. The main objective of the paper is to establish the existence and uniqueness of a strong solution and a Sobolev differentiable stochastic flow for the above SDE. Malliavin differ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03682","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"}