{"paper":{"title":"Existence and uniqueness of reflecting diffusions in cusps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cristina Costantini, Thomas G. Kurtz","submitted_at":"2017-10-17T13:48:47Z","abstract_excerpt":"We consider stochastic differential equations with (oblique) reflection in a $2$-dimensional domain that has a cusp at the origin, i..e. in a neighborhood of the origin has the form $\\{(x_1,x_2):0<x_1\\leq\\delta_0,\\psi_1(x_1)<x_2<\\psi_ 2(x_1)\\}$, with $\\psi_1(0)=\\psi_2(0)=0$, $\\psi_1'(0)=\\psi_2'(0)=0$.\n  Given a vector field $\\gamma$ of directions of reflection at the boundary points other than the origin, defining directions of reflection at the origin $\\gamma^i(0):=\\lim_{x_1\\rightarrow 0^{+}}\\gamma (x_1,\\psi_i(x_1))$, $ i=1,2,$ and assuming there exists a vector $e^{*}$ such that $\\langle e^{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.06281","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"}