{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7GVED7U7YQMZBXYWQCYCAASTDU","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":"382a067b081be2a7dc5b37e0bfbe08949ca0152f3ffca8f288957bce2c3f9e08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-16T14:35:07Z","title_canon_sha256":"55d2b1ad690547c80eb30fb4c355c06c52a4911199fef3735dbfc7595884ff58"},"schema_version":"1.0","source":{"id":"1807.05889","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.05889","created_at":"2026-07-05T00:46:01Z"},{"alias_kind":"arxiv_version","alias_value":"1807.05889v2","created_at":"2026-07-05T00:46:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.05889","created_at":"2026-07-05T00:46:01Z"},{"alias_kind":"pith_short_12","alias_value":"7GVED7U7YQMZ","created_at":"2026-07-05T00:46:01Z"},{"alias_kind":"pith_short_16","alias_value":"7GVED7U7YQMZBXYW","created_at":"2026-07-05T00:46:01Z"},{"alias_kind":"pith_short_8","alias_value":"7GVED7U7","created_at":"2026-07-05T00:46:01Z"}],"graph_snapshots":[{"event_id":"sha256:5d71dfd17363af3016f45ce812271801104bb605c9277de61fb580748a6fb182","target":"graph","created_at":"2026-07-05T00:46:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.05889/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let (Y, Z) denote the solution to a forward-backward SDE. If one constructs a random walk B n from the underlying Brownian motion B by Skorohod embedding, one can show L 2 convergence of the corresponding solutions (Y n , Z n) to (Y, Z). We estimate the rate of convergence in dependence of smoothness properties, especially for a terminal condition function in C 2,$\\alpha$. The proof relies on an approximative representation of Z n and uses the concept of discretized Malliavin calculus. Moreover, we use growth and smoothness properties of the PDE associated to the FBSDE as well as of the finite","authors_text":"Antti Luoto, C\\'eline Labart (LAMA), Christel Geiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-16T14:35:07Z","title":"Mean square rate of convergence for random walk approximation of forward-backward SDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.05889","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":"sha256:244d8f1a0da64d0f32b74a55975657ea505e422920e9512e37abf785dc5e3367","target":"record","created_at":"2026-07-05T00:46:01Z","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":"382a067b081be2a7dc5b37e0bfbe08949ca0152f3ffca8f288957bce2c3f9e08","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-16T14:35:07Z","title_canon_sha256":"55d2b1ad690547c80eb30fb4c355c06c52a4911199fef3735dbfc7595884ff58"},"schema_version":"1.0","source":{"id":"1807.05889","kind":"arxiv","version":2}},"canonical_sha256":"f9aa41fe9fc41990df1680b02002531d16084ad925224e2e49b4eeaea4feaa60","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f9aa41fe9fc41990df1680b02002531d16084ad925224e2e49b4eeaea4feaa60","first_computed_at":"2026-07-05T00:46:01.013445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:46:01.013445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D8whsc4bmwZuIuI65S8G2PokOW/7gNBY9mq9w/IqXndSrDvynizGF8ZZp/2MXk4V+6ELUG3d2ee+g8VONoH5CA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:46:01.013860Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.05889","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:244d8f1a0da64d0f32b74a55975657ea505e422920e9512e37abf785dc5e3367","sha256:5d71dfd17363af3016f45ce812271801104bb605c9277de61fb580748a6fb182"],"state_sha256":"c551323c61b4199a3d7cdf59719db9a05550258cec725fb5eab0237297f47062"}