{"paper":{"title":"Local H\\\"{o}lder continuity property of the Densities of Solutions of SDEs with Singular Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Arturo Kohatsu-Higa, Go Yuki, Masafumi Hayashi","submitted_at":"2012-06-06T03:52:20Z","abstract_excerpt":"We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H\\\"{o}lder continuous drift has a H\\\"{o}lder continuous density function. This result complements recent results of Fournier-Printems \\cite{F1}, where the density is shown to exist if both coefficients are H\\\"{o}lder continuous and exemplifies the role of the drift coefficient in the regularity of the density of a diffusion."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1117","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"}