{"paper":{"title":"A numerical approach to approximation for an ultraparabolic equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NA","math.SP"],"primary_cat":"math.AP","authors_text":"Le Trong Lan, Nguyen Huy Tuan, Nguyen Thi Yen Ngoc, Vo Anh Khoa","submitted_at":"2014-08-06T16:38:25Z","abstract_excerpt":"We study the following ultraparabolic equation\n  \\[ \\frac{\\partial}{\\partial t}u\\left(t,s\\right)+\\frac{\\partial}{\\partial s}u\\left(t,s\\right)+\\mathcal{L}u\\left(t,s\\right)=f\\left(u\\left(t,s\\right),t,s\\right),\\quad\\left(t,s\\right)\\in\\left(0,T\\right)\\times\\left(0,T\\right), \\]\n  where $\\mathcal{L}$ is a positive-definite, self-adjoint operator with compact inverse and $f$ is a nonlinear function. Mathematically, the bibliography on initial-boundary value problems for ultraparabolic equations is not extensive although the problems have many applications related to option pricing, multi parameter Br"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1351","kind":"arxiv","version":2},"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"}