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We show that the quickest detection problem \\[\\inf_{\\tau}\\bigl[\\mathsf{P}(\\tau<\\tau_{\\ell})+c\\mathsf{E}(\\tau -\\tau_{\\ell})^+\\bigr]\\] is equivalent to the (three-dimensional) optimal stopping problem \\[\\sup_{\\tau}\\mathsf{E}\\biggl[R_{\\tau}-\\int _0^{\\tau}c(R_t)\\,dt\\biggr],\\] where $R=S-I$ is the range process of $X=2"},"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":"1409.1745","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-05T11:42:51Z","cross_cats_sorted":[],"title_canon_sha256":"efb2a3b2e2cfbfdfab6573ebd909e3c7be5e45483f5807e4d154df8d1086cfdf","abstract_canon_sha256":"7c4818574506cbfc45a70485a094c1764ee91ff3f88292d6080d448a4dda2312"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:25.322762Z","signature_b64":"ATtD6/5DIJpI/HGIsF/oIsiITQzcU9jfka6riNyxsvejeV7z+vg6iEl1zC/phCBxWSgNl0k2R73Uxe1vVb5iDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3118cdc2b7e9fcd7318deb79703c4bbfa7248cff53a185a0f8a4c9dfc4f1e31b","last_reissued_at":"2026-05-18T02:43:25.322142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:25.322142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quickest detection of a hidden target and extremal surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Goran Peskir","submitted_at":"2014-09-05T11:42:51Z","abstract_excerpt":"Let $Z=(Z_t)_{t\\ge0}$ be a regular diffusion process started at $0$, let $\\ell$ be an independent random variable with a strictly increasing and continuous distribution function $F$, and let $\\tau_{\\ell}=\\inf\\{t\\ge0\\vert Z_t=\\ell\\}$ be the first entry time of $Z$ at the level $\\ell$. We show that the quickest detection problem \\[\\inf_{\\tau}\\bigl[\\mathsf{P}(\\tau<\\tau_{\\ell})+c\\mathsf{E}(\\tau -\\tau_{\\ell})^+\\bigr]\\] is equivalent to the (three-dimensional) optimal stopping problem \\[\\sup_{\\tau}\\mathsf{E}\\biggl[R_{\\tau}-\\int _0^{\\tau}c(R_t)\\,dt\\biggr],\\] where $R=S-I$ is the range process of $X=2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1745","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":"1409.1745","created_at":"2026-05-18T02:43:25.322235+00:00"},{"alias_kind":"arxiv_version","alias_value":"1409.1745v1","created_at":"2026-05-18T02:43:25.322235+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1745","created_at":"2026-05-18T02:43:25.322235+00:00"},{"alias_kind":"pith_short_12","alias_value":"GEMM3QVX5H6N","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"GEMM3QVX5H6NOMMN","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"GEMM3QVX","created_at":"2026-05-18T12:28:30.664211+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/GEMM3QVX5H6NOMMN5N4XAPCLX6","json":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6.json","graph_json":"https://pith.science/api/pith-number/GEMM3QVX5H6NOMMN5N4XAPCLX6/graph.json","events_json":"https://pith.science/api/pith-number/GEMM3QVX5H6NOMMN5N4XAPCLX6/events.json","paper":"https://pith.science/paper/GEMM3QVX"},"agent_actions":{"view_html":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6","download_json":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6.json","view_paper":"https://pith.science/paper/GEMM3QVX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1409.1745&json=true","fetch_graph":"https://pith.science/api/pith-number/GEMM3QVX5H6NOMMN5N4XAPCLX6/graph.json","fetch_events":"https://pith.science/api/pith-number/GEMM3QVX5H6NOMMN5N4XAPCLX6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/action/storage_attestation","attest_author":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/action/author_attestation","sign_citation":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/action/citation_signature","submit_replication":"https://pith.science/pith/GEMM3QVX5H6NOMMN5N4XAPCLX6/action/replication_record"}},"created_at":"2026-05-18T02:43:25.322235+00:00","updated_at":"2026-05-18T02:43:25.322235+00:00"}