{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BI2PCV5IQ2YUITRUE3EW6JNBVH","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":"c25f75e19081a18cba1fc2f9ff71499b0fb91816c3e0c74851fe45246ac0be48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-24T17:32:13Z","title_canon_sha256":"466ccc64ccdc5edd291b9ac74ec8609d80d83a64e0b0f51a0aa279cacca0972d"},"schema_version":"1.0","source":{"id":"1105.4841","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.4841","created_at":"2026-05-18T03:17:35Z"},{"alias_kind":"arxiv_version","alias_value":"1105.4841v3","created_at":"2026-05-18T03:17:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.4841","created_at":"2026-05-18T03:17:35Z"},{"alias_kind":"pith_short_12","alias_value":"BI2PCV5IQ2YU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BI2PCV5IQ2YUITRU","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BI2PCV5I","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:3edbe7018689252a8c80b25992a9b414946f16d998e9981d3ff933c971e47a10","target":"graph","created_at":"2026-05-18T03:17:35Z","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":"The purpose of this paper is to establish the convergence in law of the sequence of \"midpoint\" Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-of-variable formula in law with a second order correction term which is an It\\^{o} integral of f''(W) with respect to a Gaussian martingale independent of W. The proof of the convergence in law is based on the techniques of Malliavin calculus and uses a central limit theorem for q-fold Skorohod integrals, which is a m","authors_text":"Daniel Harnett, David Nualart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-24T17:32:13Z","title":"Central limit theorem for a Stratonovich integral with Malliavin calculus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.4841","kind":"arxiv","version":3},"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":"sha256:5a696ae2a349a26fb38e9ce9fb456495a2b109778c5befe117c177f87c0994a6","target":"record","created_at":"2026-05-18T03:17:35Z","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":"c25f75e19081a18cba1fc2f9ff71499b0fb91816c3e0c74851fe45246ac0be48","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-24T17:32:13Z","title_canon_sha256":"466ccc64ccdc5edd291b9ac74ec8609d80d83a64e0b0f51a0aa279cacca0972d"},"schema_version":"1.0","source":{"id":"1105.4841","kind":"arxiv","version":3}},"canonical_sha256":"0a34f157a886b1444e3426c96f25a1a9e966180a28f5badd076c057c84773b5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a34f157a886b1444e3426c96f25a1a9e966180a28f5badd076c057c84773b5d","first_computed_at":"2026-05-18T03:17:35.561354Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:35.561354Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l1sNdDcnEnJWFlkkQrJApVM8P8aUxHH5jP0jEAK6ycIEWOK9GStZwlhLV/22BOy/ApzBXBw35dhoY9U91W0gDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:35.561993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.4841","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a696ae2a349a26fb38e9ce9fb456495a2b109778c5befe117c177f87c0994a6","sha256:3edbe7018689252a8c80b25992a9b414946f16d998e9981d3ff933c971e47a10"],"state_sha256":"47870bc6bfe18a26ef44e578b938ec702e57f77729131913bcce5f3a3f269ae1"}