{"paper":{"title":"Smooth densities of the laws of perturbed diffusion processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lihu Xu, Tusheng Zhang, Wen Yue","submitted_at":"2016-01-23T15:02:29Z","abstract_excerpt":"Under some regularity conditions on $b$, $\\sigma$ and $\\alpha$, we prove that the following perturbed stochastic differential equation \\begin{equation} X_t=x+\\int_0^t b(X_s)ds+\\int_0^t \\sigma(X_s) dB_s+\\alpha \\sup_{0 \\le s \\le t} X_s, \\ \\ \\ \\alpha<1 \\end{equation} admits smooth densities for all $0 \\le t \\le t_0$, where $t_0>0$ is some finite number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06275","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"}