{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:LLERE35UBFGBZDT54WJRC5AEAY","short_pith_number":"pith:LLERE35U","schema_version":"1.0","canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","source":{"kind":"arxiv","id":"1603.08756","version":2},"attestation_state":"computed","paper":{"title":"Weak error analysis via functional It\\^o calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Felix Lindner, Mih\\'aly Kov\\'acs","submitted_at":"2016-03-29T13:08:05Z","abstract_excerpt":"We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\\^o calculus, such as the functional It\\^o formula and functional Kolmogorov equation, we derive a general representation formula for the weak error $E(f(X_T)-f(\\tilde X_T))$, where $X_T$ and $\\tilde X_T$ are the paths of the solution process and its approximation up to time T. The functional $f:C([0,T],R^d)\\to R$ is assumed to be twice continuously Fr\\'echet differentiable w"},"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":"1603.08756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","cross_cats_sorted":[],"title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1","abstract_canon_sha256":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:29.691690Z","signature_b64":"zP/xpC3bi9P68tra4rQCj4btHK2jivKq3dLNB5Ds3ROKYREdZlpxwqpyEd+EybZsPjhdVqhn/jXFAWDotamTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","last_reissued_at":"2026-05-18T01:12:29.691335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:29.691335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak error analysis via functional It\\^o calculus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Felix Lindner, Mih\\'aly Kov\\'acs","submitted_at":"2016-03-29T13:08:05Z","abstract_excerpt":"We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\\^o calculus, such as the functional It\\^o formula and functional Kolmogorov equation, we derive a general representation formula for the weak error $E(f(X_T)-f(\\tilde X_T))$, where $X_T$ and $\\tilde X_T$ are the paths of the solution process and its approximation up to time T. The functional $f:C([0,T],R^d)\\to R$ is assumed to be twice continuously Fr\\'echet differentiable w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08756","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":"1603.08756","created_at":"2026-05-18T01:12:29.691396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.08756v2","created_at":"2026-05-18T01:12:29.691396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08756","created_at":"2026-05-18T01:12:29.691396+00:00"},{"alias_kind":"pith_short_12","alias_value":"LLERE35UBFGB","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_16","alias_value":"LLERE35UBFGBZDT5","created_at":"2026-05-18T12:30:29.479603+00:00"},{"alias_kind":"pith_short_8","alias_value":"LLERE35U","created_at":"2026-05-18T12:30:29.479603+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/LLERE35UBFGBZDT54WJRC5AEAY","json":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY.json","graph_json":"https://pith.science/api/pith-number/LLERE35UBFGBZDT54WJRC5AEAY/graph.json","events_json":"https://pith.science/api/pith-number/LLERE35UBFGBZDT54WJRC5AEAY/events.json","paper":"https://pith.science/paper/LLERE35U"},"agent_actions":{"view_html":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY","download_json":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY.json","view_paper":"https://pith.science/paper/LLERE35U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.08756&json=true","fetch_graph":"https://pith.science/api/pith-number/LLERE35UBFGBZDT54WJRC5AEAY/graph.json","fetch_events":"https://pith.science/api/pith-number/LLERE35UBFGBZDT54WJRC5AEAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/action/storage_attestation","attest_author":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/action/author_attestation","sign_citation":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/action/citation_signature","submit_replication":"https://pith.science/pith/LLERE35UBFGBZDT54WJRC5AEAY/action/replication_record"}},"created_at":"2026-05-18T01:12:29.691396+00:00","updated_at":"2026-05-18T01:12:29.691396+00:00"}