{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:C7ZYOL67HO5SWMS3D7OAQHF3JQ","short_pith_number":"pith:C7ZYOL67","schema_version":"1.0","canonical_sha256":"17f3872fdf3bbb2b325b1fdc081cbb4c3476c89c4d95699ac0766d0bfea87d0d","source":{"kind":"arxiv","id":"1005.0616","version":3},"attestation_state":"computed","paper":{"title":"Tracking a Random Walk First-Passage Time Through Noisy Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Aslan Tchamkerten, Marat Burnashev","submitted_at":"2010-05-04T19:59:38Z","abstract_excerpt":"Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time $\\tau_\\ell$ of a given level $\\ell$ with a stopping time $\\eta$ defined over the noisy observation process.\n  Main results are upper and lower bounds on the minimum mean absolute deviation $\\inf_\\eta \\ex|\\eta-\\tau_\\ell|$ which become tight as $\\ell\\to\\infty$. Interestingly, in this regime the estimation error does not get smaller if we allow $ \\eta$ to be an arbitrary function of the entire observation process, not necessarily a stopping "},"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":"1005.0616","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2010-05-04T19:59:38Z","cross_cats_sorted":["cs.IT","math.IT","stat.TH"],"title_canon_sha256":"fab4c1e3b1bf3a219693be5e2ce99c26ebd2e9e8bade7f7305ed58d63e5bfb3e","abstract_canon_sha256":"bf875597cac0bc5173f9366446805de48a6828f09885730361fc5fcc04be3c59"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:09.051778Z","signature_b64":"IxzHm5lcbm6xepq/njJw58Zo2ZK6XAPH7cmqoFlMzZralfKfacHNnVzEx7EvZJ6X3nDuF1YVmPhVPkFv9XNsAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17f3872fdf3bbb2b325b1fdc081cbb4c3476c89c4d95699ac0766d0bfea87d0d","last_reissued_at":"2026-05-18T02:24:09.051184Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:09.051184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tracking a Random Walk First-Passage Time Through Noisy Observations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Aslan Tchamkerten, Marat Burnashev","submitted_at":"2010-05-04T19:59:38Z","abstract_excerpt":"Given a Gaussian random walk (or a Wiener process), possibly with drift, observed through noise, we consider the problem of estimating its first-passage time $\\tau_\\ell$ of a given level $\\ell$ with a stopping time $\\eta$ defined over the noisy observation process.\n  Main results are upper and lower bounds on the minimum mean absolute deviation $\\inf_\\eta \\ex|\\eta-\\tau_\\ell|$ which become tight as $\\ell\\to\\infty$. Interestingly, in this regime the estimation error does not get smaller if we allow $ \\eta$ to be an arbitrary function of the entire observation process, not necessarily a stopping "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.0616","kind":"arxiv","version":3},"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":"1005.0616","created_at":"2026-05-18T02:24:09.051266+00:00"},{"alias_kind":"arxiv_version","alias_value":"1005.0616v3","created_at":"2026-05-18T02:24:09.051266+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.0616","created_at":"2026-05-18T02:24:09.051266+00:00"},{"alias_kind":"pith_short_12","alias_value":"C7ZYOL67HO5S","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C7ZYOL67HO5SWMS3","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C7ZYOL67","created_at":"2026-05-18T12:26:05.355336+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/C7ZYOL67HO5SWMS3D7OAQHF3JQ","json":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ.json","graph_json":"https://pith.science/api/pith-number/C7ZYOL67HO5SWMS3D7OAQHF3JQ/graph.json","events_json":"https://pith.science/api/pith-number/C7ZYOL67HO5SWMS3D7OAQHF3JQ/events.json","paper":"https://pith.science/paper/C7ZYOL67"},"agent_actions":{"view_html":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ","download_json":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ.json","view_paper":"https://pith.science/paper/C7ZYOL67","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1005.0616&json=true","fetch_graph":"https://pith.science/api/pith-number/C7ZYOL67HO5SWMS3D7OAQHF3JQ/graph.json","fetch_events":"https://pith.science/api/pith-number/C7ZYOL67HO5SWMS3D7OAQHF3JQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ/action/storage_attestation","attest_author":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ/action/author_attestation","sign_citation":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ/action/citation_signature","submit_replication":"https://pith.science/pith/C7ZYOL67HO5SWMS3D7OAQHF3JQ/action/replication_record"}},"created_at":"2026-05-18T02:24:09.051266+00:00","updated_at":"2026-05-18T02:24:09.051266+00:00"}