{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:OGATACQMZWWLHC5IVFMNV52SOV","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":"dd26cc5b92bbf1b5dccaac203afbf1a6a5f4264aa20f5a52922e964ce90ccdf3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-27T19:58:03Z","title_canon_sha256":"8991c0f99cf84b8b90abda8b2ff9ca1f7171bb9b75fa8f6f45bffbfe28020281"},"schema_version":"1.0","source":{"id":"1406.7287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.7287","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"arxiv_version","alias_value":"1406.7287v3","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.7287","created_at":"2026-05-18T01:00:46Z"},{"alias_kind":"pith_short_12","alias_value":"OGATACQMZWWL","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"OGATACQMZWWLHC5I","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"OGATACQM","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:eafbf9117fdb369127e1fe1ae21a809cdb1fa8c66580b380572d274f8c54a9e0","target":"graph","created_at":"2026-05-18T01:00:46Z","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 a general multidimensional stochastic differential delay equation (SDDE) with state-dependent colored noises. We approximate it by a stochastic differential equation (SDE) system and calculate its limit as the time delays and the correlation times of the noises go to zero. The main result is proven using a theorem about convergence of stochastic integrals by Kurtz and Protter. It formalizes and extends a result that has been obtained in the analysis of a noisy electrical circuit with delayed state-dependent noise, and may be used as a working SDE approximation of an SDDE modeling a","authors_text":"Austin McDaniel, Giovanni Volpe, Jan Wehr, Ozer Duman","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-27T19:58:03Z","title":"An SDE approximation for stochastic differential delay equations with state-dependent colored noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.7287","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:f41f4275f0546bc9a5e4765714e5e2fe6d57f35dac35f4f1a0fd28f7b59ea493","target":"record","created_at":"2026-05-18T01:00:46Z","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":"dd26cc5b92bbf1b5dccaac203afbf1a6a5f4264aa20f5a52922e964ce90ccdf3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-27T19:58:03Z","title_canon_sha256":"8991c0f99cf84b8b90abda8b2ff9ca1f7171bb9b75fa8f6f45bffbfe28020281"},"schema_version":"1.0","source":{"id":"1406.7287","kind":"arxiv","version":3}},"canonical_sha256":"7181300a0ccdacb38ba8a958daf752754f947706e43720f4f45a9ee5f520f21a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7181300a0ccdacb38ba8a958daf752754f947706e43720f4f45a9ee5f520f21a","first_computed_at":"2026-05-18T01:00:46.395247Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:46.395247Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VXOOX4te/MV+86SijHpUgyZ08048hPVxfZ2dVPtGaubKWqlc4CcTYV1Vi6xJSgA/ofdH+2YmXouNjYHt1hCrBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:46.395758Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.7287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f41f4275f0546bc9a5e4765714e5e2fe6d57f35dac35f4f1a0fd28f7b59ea493","sha256:eafbf9117fdb369127e1fe1ae21a809cdb1fa8c66580b380572d274f8c54a9e0"],"state_sha256":"038433e85c43f673cc5e2904cd9107e1611a6c9386e6687a4e3cead4cbc0de18"}