{"paper":{"title":"Strong Local Nondeterminism of Spherical Fractional Brownian Motion","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Xiaohong Lan, Yimin Xiao","submitted_at":"2017-07-17T07:13:49Z","abstract_excerpt":"Let $B = \\left\\{ B\\left( x\\right),\\, x\\in \\mathbb{S}^{2}\\right\\} $ be the fractional Brownian motion indexed by the unit sphere $\\mathbb{S}^{2}$ with index $0<H\\leq \\frac{1}{2}$, introduced by Istas \\cite{IstasECP05}. We establish optimal estimates for its angular power spectrum $\\{d_\\ell, \\ell = 0, 1, 2, \\ldots\\}$, and then exploit its high-frequency behavior to establish the property of its strong local nondeterminism of $B$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.05021","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"}