{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:NSDB3WKTJVNXXV2BOHFB3LNQMC","short_pith_number":"pith:NSDB3WKT","schema_version":"1.0","canonical_sha256":"6c861dd9534d5b7bd74171ca1dadb060a280a51e9f8aa9d163b07f3675af2b6a","source":{"kind":"arxiv","id":"1507.03848","version":2},"attestation_state":"computed","paper":{"title":"Strikingly simple identities relating exit problems for L\\'evy processes under continuous and Poisson observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hansjoerg Albrecher, Jevgenijs Ivanovs","submitted_at":"2015-07-14T13:42:13Z","abstract_excerpt":"We consider exit problems for general L\\'evy processes, where the first passage over a threshold is detected either immediately or at an epoch of an independent homogeneous Poisson process. It is shown that the two corresponding one-sided problems are related through a surprisingly simple identity. Moreover, we identify a simple link between two-sided exit problems with one continuous and one Poisson exit. Finally, Poisson exit of a reflected process is connected to the continuous exit of a process reflected at Poisson epochs, and a link between some Parisian type exit problems is established."},"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":"1507.03848","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-14T13:42:13Z","cross_cats_sorted":[],"title_canon_sha256":"7cf87e5cde31f846ba1d2c1421e73c320699393f998481aa4662c2a95479e05c","abstract_canon_sha256":"32c04d0a2a9bcbf4c930426119106d8c93a1f6473956b1563e14d0b8f41e16a5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:49.407125Z","signature_b64":"b1BehEDQ1crePqEktdgIyxb0YuHiAhqLGvzpYuikKlSofVrMOYbe75Ynt5tTVGs0p03Zz3+KPra9RoNCRTpBDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c861dd9534d5b7bd74171ca1dadb060a280a51e9f8aa9d163b07f3675af2b6a","last_reissued_at":"2026-05-18T01:36:49.406519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:49.406519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strikingly simple identities relating exit problems for L\\'evy processes under continuous and Poisson observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Hansjoerg Albrecher, Jevgenijs Ivanovs","submitted_at":"2015-07-14T13:42:13Z","abstract_excerpt":"We consider exit problems for general L\\'evy processes, where the first passage over a threshold is detected either immediately or at an epoch of an independent homogeneous Poisson process. It is shown that the two corresponding one-sided problems are related through a surprisingly simple identity. Moreover, we identify a simple link between two-sided exit problems with one continuous and one Poisson exit. Finally, Poisson exit of a reflected process is connected to the continuous exit of a process reflected at Poisson epochs, and a link between some Parisian type exit problems is established."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03848","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1507.03848","created_at":"2026-05-18T01:36:49.406603+00:00"},{"alias_kind":"arxiv_version","alias_value":"1507.03848v2","created_at":"2026-05-18T01:36:49.406603+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.03848","created_at":"2026-05-18T01:36:49.406603+00:00"},{"alias_kind":"pith_short_12","alias_value":"NSDB3WKTJVNX","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"NSDB3WKTJVNXXV2B","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"NSDB3WKT","created_at":"2026-05-18T12:29:34.919912+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/NSDB3WKTJVNXXV2BOHFB3LNQMC","json":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC.json","graph_json":"https://pith.science/api/pith-number/NSDB3WKTJVNXXV2BOHFB3LNQMC/graph.json","events_json":"https://pith.science/api/pith-number/NSDB3WKTJVNXXV2BOHFB3LNQMC/events.json","paper":"https://pith.science/paper/NSDB3WKT"},"agent_actions":{"view_html":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC","download_json":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC.json","view_paper":"https://pith.science/paper/NSDB3WKT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1507.03848&json=true","fetch_graph":"https://pith.science/api/pith-number/NSDB3WKTJVNXXV2BOHFB3LNQMC/graph.json","fetch_events":"https://pith.science/api/pith-number/NSDB3WKTJVNXXV2BOHFB3LNQMC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC/action/storage_attestation","attest_author":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC/action/author_attestation","sign_citation":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC/action/citation_signature","submit_replication":"https://pith.science/pith/NSDB3WKTJVNXXV2BOHFB3LNQMC/action/replication_record"}},"created_at":"2026-05-18T01:36:49.406603+00:00","updated_at":"2026-05-18T01:36:49.406603+00:00"}