{"paper":{"title":"Extremal behaviour of hitting a cone by correlated Brownian motion with drift","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\c{e}bicki, Lanpeng Ji, Tomasz Rolski","submitted_at":"2016-10-28T20:01:56Z","abstract_excerpt":"This paper derives an exact asymptotic expression for \\[ \\mathbb{P}_{\\mathbf{x}_u}\\{\\exists_{t\\ge0} \\mathbf{X}(t)- \\boldsymbol{\\mu}t\\in \\mathcal{U} \\}, \\ \\ {\\rm as}\\ \\ u\\to\\infty, \\] where $\\mathbf{X}(t)=(X_1(t),\\ldots,X_d(t))^\\top,t\\ge0$ is a correlated $d$-dimensional Brownian motion starting at the point $\\mathbf{x}_u=-\\boldsymbol{\\alpha}u$ with $\\boldsymbol{\\alpha}\\in \\mathbb{R}^d$, $\\boldsymbol{\\mu} \\in \\mathbb{R}^d$ and $\\mathcal{U}=\\prod_{i=1}^d [0,\\infty)$. The derived asymptotics depends on the solution of an underlying multidimensional quadratic optimization problem with constraints,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.09387","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"}