{"paper":{"title":"On Piterbarg Max-discretisation Theorem for Multivariate Stationary Gaussian Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. Hashorva, Z. Tan","submitted_at":"2014-05-10T18:17:47Z","abstract_excerpt":"Let $\\{X(t), t\\geq0\\}$ be a stationary Gaussian process with zero-mean and unit variance. A deep result derived in Piterbarg (2004), which we refer to as Piterbarg's max-discretisation theorem gives the joint asymptotic behaviour ($T\\to \\infty$) of the continuous time maximum $M(T)=\\max_{t\\in [0,T]} X(t), $ and the maximum $M^{\\delta}(T)=\\max_{t\\in \\mathfrak{R}(\\delta)}X(t), $ with $\\mathfrak{R}(\\delta) \\subset [0,T]$ a uniform grid of points of distance $\\delta=\\delta(T)$. Under some asymptotic restrictions on the correlation function Piterbarg's max-discretisation theorem shows that for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2457","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"}