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We investigate the asymptotics of $$\\mathbb{P}\\left(\\sup_{t\\in \\mathcal{T} } \\min_{1\\leq i\\leq n}(X_i(t)+h_i(t))>u\\right)$$ as $u\\to\\infty$. As an illustration to the derived results we analyze two important classes of $X(t)$: with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymp"},"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":"1801.02465","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-08T15:01:24Z","cross_cats_sorted":[],"title_canon_sha256":"e6eac3d84b68a0a936130c27602a36f08d1b2660c6025c3d63e949e7efcad886","abstract_canon_sha256":"8f5bbd5c43eb665997f29fa8f036e9a7f584363964970b93486fc9f80c144161"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:31.538469Z","signature_b64":"OWWCHjJcayamAjMMmUDvg+5rQCV0Ho+336yVsi8iPLAGDNgfhOz54MqM6k71TiDYD7C2VQ5QT+Roe5a5B5TWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bf35a51edf5606d5c2d4ae23cc41933384603ceca9eb95a0d5992213841fb86","last_reissued_at":"2026-05-18T00:26:31.537753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:31.537753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremes 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":"Krzysztof Debicki, Long Bai, Peng Liu","submitted_at":"2018-01-08T15:01:24Z","abstract_excerpt":"Let $X(t)=(X_1(t), \\dots, X_n(t)), t\\in \\mathcal{T}\\subset \\mathbb{R} $ be a centered vector-valued Gaussian process with independent components and continuous trajectories, and $h(t)=(h_1(t),\\dots, h_n(t)), t\\in \\mathcal{T} $ be a vector-valued continuous function. We investigate the asymptotics of $$\\mathbb{P}\\left(\\sup_{t\\in \\mathcal{T} } \\min_{1\\leq i\\leq n}(X_i(t)+h_i(t))>u\\right)$$ as $u\\to\\infty$. As an illustration to the derived results we analyze two important classes of $X(t)$: with locally-stationary structure and with varying variances of the coordinates, and calculate exact asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02465","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1801.02465","created_at":"2026-05-18T00:26:31.537888+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.02465v1","created_at":"2026-05-18T00:26:31.537888+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02465","created_at":"2026-05-18T00:26:31.537888+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPZVUUPN6VQG","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPZVUUPN6VQG2XBN","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPZVUUPN","created_at":"2026-05-18T12:32:19.392346+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM","json":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM.json","graph_json":"https://pith.science/api/pith-number/DPZVUUPN6VQG2XBNJLRDZRAZGM/graph.json","events_json":"https://pith.science/api/pith-number/DPZVUUPN6VQG2XBNJLRDZRAZGM/events.json","paper":"https://pith.science/paper/DPZVUUPN"},"agent_actions":{"view_html":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM","download_json":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM.json","view_paper":"https://pith.science/paper/DPZVUUPN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.02465&json=true","fetch_graph":"https://pith.science/api/pith-number/DPZVUUPN6VQG2XBNJLRDZRAZGM/graph.json","fetch_events":"https://pith.science/api/pith-number/DPZVUUPN6VQG2XBNJLRDZRAZGM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM/action/storage_attestation","attest_author":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM/action/author_attestation","sign_citation":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM/action/citation_signature","submit_replication":"https://pith.science/pith/DPZVUUPN6VQG2XBNJLRDZRAZGM/action/replication_record"}},"created_at":"2026-05-18T00:26:31.537888+00:00","updated_at":"2026-05-18T00:26:31.537888+00:00"}