{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2E7DZ6QFNZ623LYNAD27FOCEWC","short_pith_number":"pith:2E7DZ6QF","schema_version":"1.0","canonical_sha256":"d13e3cfa056e7dadaf0d00f5f2b844b091d784f3046cc43a6bd11a4af499b881","source":{"kind":"arxiv","id":"1704.01563","version":1},"attestation_state":"computed","paper":{"title":"On Extremal Index of max-stable stationary processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\k{e}bicki","submitted_at":"2017-04-05T17:57:29Z","abstract_excerpt":"In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process $W(t),t\\in R$ as $$\\mathcal{H}_W^\\delta= \\lim_{T\\to\\infty} T^{-1} E{ \\left(\\sup_{t\\in \\delta Z \\cap [0,T]} e^{W(t)}\\right) },\\ \\delta \\ge 0$$ (set $0 Z=R$ if $\\delta=0$) and the extremal index of the associated max-stable stationary process $\\xi_W$. We derive several new formulas and obtain lower bounds for $\\mathcal{H}_W^\\delta$ if $W$ is a Gaussian or a L\\'evy process. As a by-product we show an interesting relation between Pickands constants and lower tail probab"},"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":"1704.01563","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-05T17:57:29Z","cross_cats_sorted":[],"title_canon_sha256":"7b68c36da5b38650d6029eca5f36503cce10ff33a3c6ec6e9da83edaed25e5af","abstract_canon_sha256":"2a8f79e68acdccb26813d148db756012fb3b7578b72fd5381914be25a44d91c3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:56.141593Z","signature_b64":"Bs/7L3iuMfAxJ+F19l2fp11O9QTNBSsFezpeaDWJWZWlq0MUi7cJp91aGjZqcAtDUD9yqSRhKgc5E9zwCsgODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d13e3cfa056e7dadaf0d00f5f2b844b091d784f3046cc43a6bd11a4af499b881","last_reissued_at":"2026-05-18T00:46:56.141023Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:56.141023Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Extremal Index of max-stable stationary processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Enkelejd Hashorva, Krzysztof D\\k{e}bicki","submitted_at":"2017-04-05T17:57:29Z","abstract_excerpt":"In this contribution we discuss the relation between Pickands-type constants defined for certain Brown-Resnick stationary process $W(t),t\\in R$ as $$\\mathcal{H}_W^\\delta= \\lim_{T\\to\\infty} T^{-1} E{ \\left(\\sup_{t\\in \\delta Z \\cap [0,T]} e^{W(t)}\\right) },\\ \\delta \\ge 0$$ (set $0 Z=R$ if $\\delta=0$) and the extremal index of the associated max-stable stationary process $\\xi_W$. We derive several new formulas and obtain lower bounds for $\\mathcal{H}_W^\\delta$ if $W$ is a Gaussian or a L\\'evy process. As a by-product we show an interesting relation between Pickands constants and lower tail probab"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01563","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":"1704.01563","created_at":"2026-05-18T00:46:56.141119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.01563v1","created_at":"2026-05-18T00:46:56.141119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01563","created_at":"2026-05-18T00:46:56.141119+00:00"},{"alias_kind":"pith_short_12","alias_value":"2E7DZ6QFNZ62","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2E7DZ6QFNZ623LYN","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2E7DZ6QF","created_at":"2026-05-18T12:30:55.937587+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/2E7DZ6QFNZ623LYNAD27FOCEWC","json":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC.json","graph_json":"https://pith.science/api/pith-number/2E7DZ6QFNZ623LYNAD27FOCEWC/graph.json","events_json":"https://pith.science/api/pith-number/2E7DZ6QFNZ623LYNAD27FOCEWC/events.json","paper":"https://pith.science/paper/2E7DZ6QF"},"agent_actions":{"view_html":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC","download_json":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC.json","view_paper":"https://pith.science/paper/2E7DZ6QF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.01563&json=true","fetch_graph":"https://pith.science/api/pith-number/2E7DZ6QFNZ623LYNAD27FOCEWC/graph.json","fetch_events":"https://pith.science/api/pith-number/2E7DZ6QFNZ623LYNAD27FOCEWC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC/action/storage_attestation","attest_author":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC/action/author_attestation","sign_citation":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC/action/citation_signature","submit_replication":"https://pith.science/pith/2E7DZ6QFNZ623LYNAD27FOCEWC/action/replication_record"}},"created_at":"2026-05-18T00:46:56.141119+00:00","updated_at":"2026-05-18T00:46:56.141119+00:00"}