{"paper":{"title":"Boundary Non-Crossings of Additive Wiener Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Yuliya Mishura","submitted_at":"2014-02-11T20:13:09Z","abstract_excerpt":"Let $W_i=\\{W_i(t), t\\in \\mathbb{R}_+\\}, i=1,2$ be two Wiener processes and $W_3=\\{W_3(\\mathbf{t}), \\mathbf{t}\\in \\mathbb{R}_+^2\\}$ be a two-parameter Brownian sheet, all three processes being mutually independent. We derive upper and lower bounds for the boundary non-crossing probability $$P_f=P\\{W_1(t_1)+W_2(t_2)+W_3(\\mathbf{t})+h(\\mathbf{t})\\leq u(\\mathbf{t}), \\mathbf{t}\\in\\mathbb{R}_+^2\\},$$ where $h, u: \\mathbb{R}_+^2\\rightarrow \\mathbb{R}_+$ are two measurable functions. We show further that for large trend functions $\\gamma f>0$ asymptotically when $\\gamma \\to \\infty$ we have that $\\ln P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.2620","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"}