{"paper":{"title":"Spectral conditions for strong local nondeterminism and exact Hausdorff measure of ranges of Gaussian random fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nana Luan, Yimin Xiao","submitted_at":"2011-09-09T20:52:05Z","abstract_excerpt":"Let $X= \\{X(t), t \\in \\R^N\\}$ be a Gaussian random field with values in $\\R^d$ defined by \\[ X(t) = \\big(X_1(t),..., X_d(t)\\big),\\qquad t \\in \\R^N, \\] where $X_1, ..., X_d$ are independent copies of a real-valued, centered, anisotropic Gaussian random field $X_0$ which has stationary increments and the property of strong local nondeterminism. In this paper we determine the exact Hausdorff measure function for the range $X([0, 1]^N)$.\n  We also provide a sufficient condition for a Gaussian random field with stationary increments to be strongly locally nondeterministic. This condition is given i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2157","kind":"arxiv","version":1},"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"}