{"paper":{"title":"A Note on One-dimensional Stochastic Differential Equations with Generalized Drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hans-J\\\"urgen Engelbert, Stefan Blei","submitted_at":"2012-08-15T10:11:51Z","abstract_excerpt":"We consider one-dimensional stochastic differential equations with generalized drift which involve the local time $L^X$ of the solution process:\n  X_t = X_0 + \\int_0^t b(X_s) dB_s + \\int_\\mathbb{R} L^X(t,y) \\nu(dy),\nwhere b is a measurable real function, $B$ is a Wiener process and $\\nu$ denotes a set function which is defined on the bounded Borel sets of the real line $\\mathbb{R}$ such that it is a finite signed measure on $\\mathscr{B}([-N,N])$ for every $N \\in \\mathbb{N}$. This kind of equation is, in dependence of using the right, the left or the symmetric local time, usually studied under "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3078","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"}