{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:S2ANDRY4D7JLZLHOMK6UC2W5TE","short_pith_number":"pith:S2ANDRY4","schema_version":"1.0","canonical_sha256":"9680d1c71c1fd2bcacee62bd416add991bf8e7093b9895c0202042716dcc8ad2","source":{"kind":"arxiv","id":"1610.05225","version":1},"attestation_state":"computed","paper":{"title":"Estimation error for occupation time functionals of stationary Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jakub Chorowski, Randolf Altmeyer","submitted_at":"2016-10-17T17:44:23Z","abstract_excerpt":"The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better understanding of the estimation error and to prove a general error bound. The presented approach admits general integrands and gives a unifying explanation for different rates obtained in the literature. Several examples demonstrate how the general bound can be related to well-known function spaces."},"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":"1610.05225","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-10-17T17:44:23Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"90d47952ebc05c77a88b4fd522d5858d5f98a8244f3472fe22779559ecd86128","abstract_canon_sha256":"76105b5c08eda3cb9bac40c1f8889a639156af88f8823b273e72af02d9be6b4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:05.810078Z","signature_b64":"puosNF1kJSunFYojGd2W37vBGebUn4UlkYrOHA1LZvk3xLan82ranO+MEE7e07F6ceL6U52YFtrhC/YuGk09BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9680d1c71c1fd2bcacee62bd416add991bf8e7093b9895c0202042716dcc8ad2","last_reissued_at":"2026-05-18T01:02:05.809537Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:05.809537Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Estimation error for occupation time functionals of stationary Markov processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jakub Chorowski, Randolf Altmeyer","submitted_at":"2016-10-17T17:44:23Z","abstract_excerpt":"The approximation of integral functionals with respect to a stationary Markov process by a Riemann-sum estimator is studied. Stationarity and the functional calculus of the infinitesimal generator of the process are used to get a better understanding of the estimation error and to prove a general error bound. The presented approach admits general integrands and gives a unifying explanation for different rates obtained in the literature. Several examples demonstrate how the general bound can be related to well-known function spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05225","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":"1610.05225","created_at":"2026-05-18T01:02:05.809622+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.05225v1","created_at":"2026-05-18T01:02:05.809622+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.05225","created_at":"2026-05-18T01:02:05.809622+00:00"},{"alias_kind":"pith_short_12","alias_value":"S2ANDRY4D7JL","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_16","alias_value":"S2ANDRY4D7JLZLHO","created_at":"2026-05-18T12:30:41.710351+00:00"},{"alias_kind":"pith_short_8","alias_value":"S2ANDRY4","created_at":"2026-05-18T12:30:41.710351+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/S2ANDRY4D7JLZLHOMK6UC2W5TE","json":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE.json","graph_json":"https://pith.science/api/pith-number/S2ANDRY4D7JLZLHOMK6UC2W5TE/graph.json","events_json":"https://pith.science/api/pith-number/S2ANDRY4D7JLZLHOMK6UC2W5TE/events.json","paper":"https://pith.science/paper/S2ANDRY4"},"agent_actions":{"view_html":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE","download_json":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE.json","view_paper":"https://pith.science/paper/S2ANDRY4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.05225&json=true","fetch_graph":"https://pith.science/api/pith-number/S2ANDRY4D7JLZLHOMK6UC2W5TE/graph.json","fetch_events":"https://pith.science/api/pith-number/S2ANDRY4D7JLZLHOMK6UC2W5TE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE/action/storage_attestation","attest_author":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE/action/author_attestation","sign_citation":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE/action/citation_signature","submit_replication":"https://pith.science/pith/S2ANDRY4D7JLZLHOMK6UC2W5TE/action/replication_record"}},"created_at":"2026-05-18T01:02:05.809622+00:00","updated_at":"2026-05-18T01:02:05.809622+00:00"}