{"paper":{"title":"Piterbarg Theorems for Chi-processes with Trend","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Lanpeng Ji","submitted_at":"2013-09-01T20:00:58Z","abstract_excerpt":"Let $\\chi_n(t) = (\\sum_{i=1}^n X_i^2(t))^{1/2},t\\ge0$ be a chi-process with $n$ degrees of freedom where $X_i$'s are independent copies of some generic centered Gaussian process $X$. This paper derives the exact asymptotic behavior of P{\\sup_{t\\in[0,T]} \\chi_n(t)>u} as u \\to \\infty, where $T$ is a given positive constant, and $g(\\cdot)$ is some non-negative bounded measurable function. The case $g(t)\\equiv0$ is investigated in numerous contributions by V.I. Piterbarg. Our novel asymptotic results for both stationary and non-stationary $X$are referred to as Piterbarg theorems for chi-processes "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.0255","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"}