{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:JN5DRCVI7L7FCPDWC33ON6WRBM","short_pith_number":"pith:JN5DRCVI","canonical_record":{"source":{"id":"1609.07431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T17:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"b34942575e1cf4e3d0a7fb9e8ebfa65b6cb9eeb76f820a5c3e30a3217d696e16","abstract_canon_sha256":"e5cb26422f31036a484b4d844b139de45538d5959317a1a3948741eaf39399c6"},"schema_version":"1.0"},"canonical_sha256":"4b7a388aa8fafe513c7616f6e6fad10b144e1ca52d2d2db481295ed60dc5c4ab","source":{"kind":"arxiv","id":"1609.07431","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07431","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07431v3","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07431","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"pith_short_12","alias_value":"JN5DRCVI7L7F","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JN5DRCVI7L7FCPDW","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JN5DRCVI","created_at":"2026-05-18T12:30:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:JN5DRCVI7L7FCPDWC33ON6WRBM","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07431","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T17:01:20Z","cross_cats_sorted":[],"title_canon_sha256":"b34942575e1cf4e3d0a7fb9e8ebfa65b6cb9eeb76f820a5c3e30a3217d696e16","abstract_canon_sha256":"e5cb26422f31036a484b4d844b139de45538d5959317a1a3948741eaf39399c6"},"schema_version":"1.0"},"canonical_sha256":"4b7a388aa8fafe513c7616f6e6fad10b144e1ca52d2d2db481295ed60dc5c4ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:56.632174Z","signature_b64":"mj71H9uhNNXxC0BIHTY9oBjLvQL0i+dq1t/Fcs2RYV5hgnLSizjPd/8dclbhwFUjb00TIXH4BubotTcioZ2rCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b7a388aa8fafe513c7616f6e6fad10b144e1ca52d2d2db481295ed60dc5c4ab","last_reissued_at":"2026-05-18T00:50:56.631652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:56.631652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07431","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YeVmP5lYgGgtzVc4zHrDdqq2CLh4jTiS52hY4GmOvLiJ70Fwyw+7PGHut6Dy6nsctq12qYIsgEdiPInhVYVlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:32:47.584226Z"},"content_sha256":"62b5eb7871c1e260cd3898be523f4a677e1d5f8509ee113712f60405b51e8e04","schema_version":"1.0","event_id":"sha256:62b5eb7871c1e260cd3898be523f4a677e1d5f8509ee113712f60405b51e8e04"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:JN5DRCVI7L7FCPDWC33ON6WRBM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An unbiased Monte Carlo estimator for derivatives. Application to CIR","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Etienne Tanr\\'e, Victor Reutenauer","submitted_at":"2016-09-23T17:01:20Z","abstract_excerpt":"In this paper, we present extensions of the exact simulation algorithm introduced by Beskos et al. (2006). First, a modification in the order in which the simulation is done accelerates the algorithm. In addition, we propose a truncated version of the modified algorithm. We obtain a control of the bias of this last version, exponentially small in function of the truncation parameter. Then, we extend it to more general drift functions. Our main result is an unbiased algorithm to approximate the two first derivatives with respect to the initial condition \\(x\\) of quantities with the form \\(\\math"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07431","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B4RdJJk8AKi0MUw7eOZ9oKJd2R2r3w8Z+AzmnEdH2F5ZdV2RjxtNX8/j0opZtS55n6rEY9pSA/6dqtdY/qWADg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T13:32:47.584591Z"},"content_sha256":"8f2755725e51c360a2581287c004fc9ad8ba4b0076bab63367806805e5605fa6","schema_version":"1.0","event_id":"sha256:8f2755725e51c360a2581287c004fc9ad8ba4b0076bab63367806805e5605fa6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JN5DRCVI7L7FCPDWC33ON6WRBM/bundle.json","state_url":"https://pith.science/pith/JN5DRCVI7L7FCPDWC33ON6WRBM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JN5DRCVI7L7FCPDWC33ON6WRBM/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T13:32:47Z","links":{"resolver":"https://pith.science/pith/JN5DRCVI7L7FCPDWC33ON6WRBM","bundle":"https://pith.science/pith/JN5DRCVI7L7FCPDWC33ON6WRBM/bundle.json","state":"https://pith.science/pith/JN5DRCVI7L7FCPDWC33ON6WRBM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JN5DRCVI7L7FCPDWC33ON6WRBM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:JN5DRCVI7L7FCPDWC33ON6WRBM","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":"e5cb26422f31036a484b4d844b139de45538d5959317a1a3948741eaf39399c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T17:01:20Z","title_canon_sha256":"b34942575e1cf4e3d0a7fb9e8ebfa65b6cb9eeb76f820a5c3e30a3217d696e16"},"schema_version":"1.0","source":{"id":"1609.07431","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07431","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07431v3","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07431","created_at":"2026-05-18T00:50:56Z"},{"alias_kind":"pith_short_12","alias_value":"JN5DRCVI7L7F","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_16","alias_value":"JN5DRCVI7L7FCPDW","created_at":"2026-05-18T12:30:25Z"},{"alias_kind":"pith_short_8","alias_value":"JN5DRCVI","created_at":"2026-05-18T12:30:25Z"}],"graph_snapshots":[{"event_id":"sha256:8f2755725e51c360a2581287c004fc9ad8ba4b0076bab63367806805e5605fa6","target":"graph","created_at":"2026-05-18T00:50:56Z","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":"In this paper, we present extensions of the exact simulation algorithm introduced by Beskos et al. (2006). First, a modification in the order in which the simulation is done accelerates the algorithm. In addition, we propose a truncated version of the modified algorithm. We obtain a control of the bias of this last version, exponentially small in function of the truncation parameter. Then, we extend it to more general drift functions. Our main result is an unbiased algorithm to approximate the two first derivatives with respect to the initial condition \\(x\\) of quantities with the form \\(\\math","authors_text":"Etienne Tanr\\'e, Victor Reutenauer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T17:01:20Z","title":"An unbiased Monte Carlo estimator for derivatives. Application to CIR"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07431","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":"sha256:62b5eb7871c1e260cd3898be523f4a677e1d5f8509ee113712f60405b51e8e04","target":"record","created_at":"2026-05-18T00:50:56Z","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":"e5cb26422f31036a484b4d844b139de45538d5959317a1a3948741eaf39399c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-23T17:01:20Z","title_canon_sha256":"b34942575e1cf4e3d0a7fb9e8ebfa65b6cb9eeb76f820a5c3e30a3217d696e16"},"schema_version":"1.0","source":{"id":"1609.07431","kind":"arxiv","version":3}},"canonical_sha256":"4b7a388aa8fafe513c7616f6e6fad10b144e1ca52d2d2db481295ed60dc5c4ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b7a388aa8fafe513c7616f6e6fad10b144e1ca52d2d2db481295ed60dc5c4ab","first_computed_at":"2026-05-18T00:50:56.631652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:56.631652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mj71H9uhNNXxC0BIHTY9oBjLvQL0i+dq1t/Fcs2RYV5hgnLSizjPd/8dclbhwFUjb00TIXH4BubotTcioZ2rCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:56.632174Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07431","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62b5eb7871c1e260cd3898be523f4a677e1d5f8509ee113712f60405b51e8e04","sha256:8f2755725e51c360a2581287c004fc9ad8ba4b0076bab63367806805e5605fa6"],"state_sha256":"48d6e9d95c3f6d319657abdfa6cff76fb68270a4b9dc36af62fed0bd972859f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"L5JhMv0CALfCnpdRoNj6L1ICOiOpVMRMTBtI1Fiw9klspfuqo0vMRb0WLXWTVnRWdOjwVo+UZyfbMU//0JtVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T13:32:47.586557Z","bundle_sha256":"edac0ed476c862b2aeddfd645e5512100f48edba3378d8bfd9feedb03780361a"}}