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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1309.0255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-01T20:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"8153b88feaeed753e1915cb8f79881532b81c13721f57563a9cff8f22b1812bb","abstract_canon_sha256":"a568e848ed6e00f613074242675fa37afba1c38b176e41d50b3add19d153820c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:27.722591Z","signature_b64":"0vXWq0NTkwjSyuUwCevY/Z7RM/t8UjjoNheiALcQrJNwbgJosn0CxQuu1yoGqi+Q8kPJr7jzobbnjHA4IuIODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d8e74dfe6203856c9e87a64cc950645a484478613cbff9478a5088eb5ea6030","last_reissued_at":"2026-05-18T03:14:27.722025Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:27.722025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $X$. 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