{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LTDSHL3HSLAFG2QIWSNLHIHPPA","short_pith_number":"pith:LTDSHL3H","schema_version":"1.0","canonical_sha256":"5cc723af6792c0536a08b49ab3a0ef7835181015db8ece9daf2bdb9907cbd3cf","source":{"kind":"arxiv","id":"1711.08012","version":1},"attestation_state":"computed","paper":{"title":"A high order time discretization of the solution of the non-linear filtering problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dan Crisan, Salvador Ortiz-Latorre","submitted_at":"2017-11-21T19:48:05Z","abstract_excerpt":"The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization schemes of these functionals of arbitrary order. The result generalizes the classical work of Picard, who introduced first order discretizations to the filtering functionals. For a given time interval partition, we construct discretization schemes with convergence rates that are proportional with the $m$-power of the mesh of the partition for arbitrary $m\\in\\math"},"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":"1711.08012","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-11-21T19:48:05Z","cross_cats_sorted":[],"title_canon_sha256":"8107f2fe190e3de5143cbe194713c2b857a784433fa700047420afcfe0dabe2b","abstract_canon_sha256":"9bc5d6b5c8ba21d25f07fdfe18205dfb661134b83aa87f603e3e03decf152124"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:50.930706Z","signature_b64":"KxcMSDO/sINW0IyN7WQcOC7sJLmwqGUStxC498jag/jeWz8PxG5DivdQNzH5AFZs9+NzbNdZimj/gHd0g0MACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5cc723af6792c0536a08b49ab3a0ef7835181015db8ece9daf2bdb9907cbd3cf","last_reissued_at":"2026-05-18T00:29:50.930093Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:50.930093Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A high order time discretization of the solution of the non-linear filtering problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dan Crisan, Salvador Ortiz-Latorre","submitted_at":"2017-11-21T19:48:05Z","abstract_excerpt":"The solution of the continuous time filtering problem can be represented as a ratio of two expectations of certain functionals of the signal process that are parametrized by the observation path. We introduce a class of discretization schemes of these functionals of arbitrary order. The result generalizes the classical work of Picard, who introduced first order discretizations to the filtering functionals. For a given time interval partition, we construct discretization schemes with convergence rates that are proportional with the $m$-power of the mesh of the partition for arbitrary $m\\in\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08012","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":"1711.08012","created_at":"2026-05-18T00:29:50.930185+00:00"},{"alias_kind":"arxiv_version","alias_value":"1711.08012v1","created_at":"2026-05-18T00:29:50.930185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.08012","created_at":"2026-05-18T00:29:50.930185+00:00"},{"alias_kind":"pith_short_12","alias_value":"LTDSHL3HSLAF","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LTDSHL3HSLAFG2QI","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LTDSHL3H","created_at":"2026-05-18T12:31:28.150371+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/LTDSHL3HSLAFG2QIWSNLHIHPPA","json":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA.json","graph_json":"https://pith.science/api/pith-number/LTDSHL3HSLAFG2QIWSNLHIHPPA/graph.json","events_json":"https://pith.science/api/pith-number/LTDSHL3HSLAFG2QIWSNLHIHPPA/events.json","paper":"https://pith.science/paper/LTDSHL3H"},"agent_actions":{"view_html":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA","download_json":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA.json","view_paper":"https://pith.science/paper/LTDSHL3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1711.08012&json=true","fetch_graph":"https://pith.science/api/pith-number/LTDSHL3HSLAFG2QIWSNLHIHPPA/graph.json","fetch_events":"https://pith.science/api/pith-number/LTDSHL3HSLAFG2QIWSNLHIHPPA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA/action/storage_attestation","attest_author":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA/action/author_attestation","sign_citation":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA/action/citation_signature","submit_replication":"https://pith.science/pith/LTDSHL3HSLAFG2QIWSNLHIHPPA/action/replication_record"}},"created_at":"2026-05-18T00:29:50.930185+00:00","updated_at":"2026-05-18T00:29:50.930185+00:00"}