{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:Z7PZ4RR3LMKY2FWIZEM7HQ3YQY","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":"c1929b03b50924e5ba1d42cff9e5e574e40bd1378b48e6ac78ad55ee191b46af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T05:34:40Z","title_canon_sha256":"d0c47dfd8a7ed9b659826be65df978b29cbd2834f61f5116f67b15a831ba6d9a"},"schema_version":"1.0","source":{"id":"1710.05277","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.05277","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"arxiv_version","alias_value":"1710.05277v5","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.05277","created_at":"2026-05-18T00:03:29Z"},{"alias_kind":"pith_short_12","alias_value":"Z7PZ4RR3LMKY","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"Z7PZ4RR3LMKY2FWI","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"Z7PZ4RR3","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:80f962b05e92bd6505b0d78d92454332a6fd04bbecee01543ad1b5ad81dc6331","target":"graph","created_at":"2026-05-18T00:03:29Z","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":"For a family of stochastic differential equations, we investigate the asymptotic behaviors of its corresponding Picard's iteration, establishing convergence results in terms of relative entropy. Our convergence results complement the conventional ones in the $L^2$ and almost sure sense, revealing some previously unexplored aspects of the stochastic differential equations under consideration. For example, in combination with Pinsker's inequality, one of our results readily yields the convergence under Picard's iteration in the total variation sense, which does not seem to directly follow from a","authors_text":"Guangyue Han, Tsz Hin Ng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T05:34:40Z","title":"Relative entropy convergence under Picard's iteration for stochastic differential equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.05277","kind":"arxiv","version":5},"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":"sha256:344005bfba2400b7f7f91d655ec3dac279b84e174160961f04989d599139da79","target":"record","created_at":"2026-05-18T00:03:29Z","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":"c1929b03b50924e5ba1d42cff9e5e574e40bd1378b48e6ac78ad55ee191b46af","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-15T05:34:40Z","title_canon_sha256":"d0c47dfd8a7ed9b659826be65df978b29cbd2834f61f5116f67b15a831ba6d9a"},"schema_version":"1.0","source":{"id":"1710.05277","kind":"arxiv","version":5}},"canonical_sha256":"cfdf9e463b5b158d16c8c919f3c3788616000b10b8080e5d84c3d6d10c83c575","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfdf9e463b5b158d16c8c919f3c3788616000b10b8080e5d84c3d6d10c83c575","first_computed_at":"2026-05-18T00:03:29.557151Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:29.557151Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ROgtjZlLrgPHzHqhef2UBpxf9by+25KR/r6yA3pUcg36YQnU1Ur+BkcTPVkNChsMef+CJINCKMVujCN6nZuuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:29.557879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.05277","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:344005bfba2400b7f7f91d655ec3dac279b84e174160961f04989d599139da79","sha256:80f962b05e92bd6505b0d78d92454332a6fd04bbecee01543ad1b5ad81dc6331"],"state_sha256":"9bd36160a0e8ded0d9224430756d785415072d5ea5e9b934ccc5168b6581d49b"}