{"paper":{"title":"Tail Asymptotics for the Extremes of Bivariate Gaussian Random Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Yimin Xiao, Yuzhen Zhou","submitted_at":"2015-04-29T04:19:42Z","abstract_excerpt":"Let $\\{X(t)= (X_1(t),X_2(t))^T,\\ t \\in \\mathbb{R}^N\\}$ be an $\\mathbb{R}^2$-valued continuous locally stationary Gaussian random field with $\\mathbb{E}[X(t)]=\\mathbf{0}$. For any compact sets $A_1, A_2 \\subset \\mathbb{R}^N$, precise asymptotic behavior of the excursion probability \\[ \\mathbb{P}\\bigg(\\max_{s\\in A_1} X_1(s)>u,\\, \\max_{t\\in A_2} X_2(t)>u\\bigg),\\ \\ \\text{ as }\\ u \\rightarrow \\infty \\] is investigated by applying the double sum method. The explicit results depend not only on the smoothness parameters of the coordinate fields $X_1$ and $X_2$, but also on their maximum correlation $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07717","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"}