{"paper":{"title":"Extremes of Spherical Fractional Brownian Motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dan Cheng, Peng Liu","submitted_at":"2018-06-08T04:27:59Z","abstract_excerpt":"Let $\\{B_\\beta (x), x \\in \\mathbb{S}^N\\}$ be a fractional Brownian motion on the $N$-dimensional unit sphere $\\mathbb{S}^N$ with Hurst index $\\beta$. We study the excursion probability $\\mathbb{P}\\{\\sup_{x\\in T} B_\\beta(x) > u \\}$ and obtain the asymptotics as $u\\to \\infty$, where $T$ can be the entire sphere $\\mathbb{S}^N$ or a geodesic disc on $\\mathbb{S}^N$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02965","kind":"arxiv","version":4},"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"}