{"paper":{"title":"Extremes of $L^p$-norm of Vector-valued Gaussian processes with Trend","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Long Bai","submitted_at":"2017-06-26T13:27:34Z","abstract_excerpt":"Let $\\boldsymbol{X}(t)=(X_1(t),\\ldots,X_d(t))$ be a Gaussian vector process and $g(t)$ be a continuous function. The asymptotics of distribution of $\\left\\|\\boldsymbol{X}(t)\\right\\|_p$, the $L^p$ norm for Gaussian finite-dimensional vector, have been investigated in numerous literatures. In this contribution we are concerned with the exact tail asymptotics of $\\left\\|\\boldsymbol{X}(t)\\right\\|^c_p,\\ c>0, $ with trend $g(t)$ over $[0,T]$. Both scenarios that $\\boldsymbol{X}(t)$ is locally stationary and non-stationary are considered. Important examples include $\\sum_{i=1}^d \\left|X_i(t)\\right|+g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08360","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"}