{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:SSNJHRI5TW7QTXCDRE34OX33WV","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":"df3b4cc338319d5307877b817f68f9e670df8d2af179dffbd28289cca48ab4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","title_canon_sha256":"8e586838ecea264e51b4dd3993b351c10cb4b1f7066bc4ae27452e65c67cd6da"},"schema_version":"1.0","source":{"id":"1208.1908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.1908","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"arxiv_version","alias_value":"1208.1908v1","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.1908","created_at":"2026-05-18T03:27:03Z"},{"alias_kind":"pith_short_12","alias_value":"SSNJHRI5TW7Q","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"SSNJHRI5TW7QTXCD","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"SSNJHRI5","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:bf1db2168010fa7a6d1fba2ae22d6a12296ff50acdc588fb5fcbcd000ff4cd9b","target":"graph","created_at":"2026-05-18T03:27:03Z","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 construct an iterated stochastic integral with fractional Brownian motion with H > 1/2. The first integrand is a deterministic function, and each successive integral is with respect to an independent fBm. We show that this symmetric stochastic integral is equal to the Malliavin divergence integral. By a version of the Fourth Moment theorem of Nualart and Peccati, we show that a family of such integrals converges in distribution to a scaled Brownian motion. An application is an approximation to the windings for a planar fBm, previously studied by Baudoin and Nualart.","authors_text":"Daniel Harnett, David Nualart","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","title":"CLT for an iterated integral with respect to fBm with H > 1/2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.1908","kind":"arxiv","version":1},"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":"sha256:85dc9e456ecab75b00b2372146e95e2ae636b00dae53d56a07fde43b0368d215","target":"record","created_at":"2026-05-18T03:27:03Z","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":"df3b4cc338319d5307877b817f68f9e670df8d2af179dffbd28289cca48ab4f0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-09T13:44:34Z","title_canon_sha256":"8e586838ecea264e51b4dd3993b351c10cb4b1f7066bc4ae27452e65c67cd6da"},"schema_version":"1.0","source":{"id":"1208.1908","kind":"arxiv","version":1}},"canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"949a93c51d9dbf09dc438937c75f7bb57a3411c17df91f0856541364368b8546","first_computed_at":"2026-05-18T03:27:03.406938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:03.406938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VnT2MqskZOC/ygwuNDIAHGHRalmaNn5XAX0mZwFgRDYn85mnJV9s7kmCuSRXBcIkI0bFT4fkD+qMOd29//+ADA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:03.407516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.1908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:85dc9e456ecab75b00b2372146e95e2ae636b00dae53d56a07fde43b0368d215","sha256:bf1db2168010fa7a6d1fba2ae22d6a12296ff50acdc588fb5fcbcd000ff4cd9b"],"state_sha256":"9d00703f5250ceb2e0414cbd2327736aea788f4236c3b5f455d657a064e06bfb"}