{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LLERE35UBFGBZDT54WJRC5AEAY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1"},"schema_version":"1.0","source":{"id":"1603.08756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08756","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08756v2","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08756","created_at":"2026-05-18T01:12:29Z"},{"alias_kind":"pith_short_12","alias_value":"LLERE35UBFGB","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LLERE35UBFGBZDT5","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LLERE35U","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:331be73e97377356cce3d9d269f4db80e3ecbd7002b5301b4aa52f61c9acdd28","target":"graph","created_at":"2026-05-18T01:12:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Felix Lindner, Mih\\'aly Kov\\'acs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","title":"Weak error analysis via functional It\\^o calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08756","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2a7cff83332a56cc1880135ba05e5e989f11b9fa3855a68cb54d43fbe405d3ba","target":"record","created_at":"2026-05-18T01:12:29Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0c05f87e630e02cfc48b86d4c3bb20425df1dfaf1994e0a6cf28dfd72d2ca5d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-29T13:08:05Z","title_canon_sha256":"dfce4e33b41e654bc341b6668eedadb49b34ed2cafc0bb79d8ce937a830c14e1"},"schema_version":"1.0","source":{"id":"1603.08756","kind":"arxiv","version":2}},"canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ac9126fb4094c1c8e7de593117404060db9b0efb8c4271efa43b36573730b19","first_computed_at":"2026-05-18T01:12:29.691335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:29.691335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zP/xpC3bi9P68tra4rQCj4btHK2jivKq3dLNB5Ds3ROKYREdZlpxwqpyEd+EybZsPjhdVqhn/jXFAWDotamTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:29.691690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a7cff83332a56cc1880135ba05e5e989f11b9fa3855a68cb54d43fbe405d3ba","sha256:331be73e97377356cce3d9d269f4db80e3ecbd7002b5301b4aa52f61c9acdd28"],"state_sha256":"555fdf16e5bc6fe5a1fe481e616a04ed834eae3d893e428b70a425d8b9b27cfc"}