{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B6H2L3TK2YCKZLLTNF2LCEINZ7","short_pith_number":"pith:B6H2L3TK","canonical_record":{"source":{"id":"1710.07492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-20T11:30:02Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"23ea5244c31a253b9702d04a3d9dcd3ed1a7c52a2a959dfa6d30756a93f41c03","abstract_canon_sha256":"8f56b1209d8f2c2438ae25544af31bd649d82e7d3797aef7c31451abd360019a"},"schema_version":"1.0"},"canonical_sha256":"0f8fa5ee6ad604acad736974b1110dcff9a76b78ef2334ffb2e87414117d7d86","source":{"kind":"arxiv","id":"1710.07492","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07492","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07492v2","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07492","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"B6H2L3TK2YCK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B6H2L3TK2YCKZLLT","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B6H2L3TK","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B6H2L3TK2YCKZLLTNF2LCEINZ7","target":"record","payload":{"canonical_record":{"source":{"id":"1710.07492","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-20T11:30:02Z","cross_cats_sorted":["q-fin.CP"],"title_canon_sha256":"23ea5244c31a253b9702d04a3d9dcd3ed1a7c52a2a959dfa6d30756a93f41c03","abstract_canon_sha256":"8f56b1209d8f2c2438ae25544af31bd649d82e7d3797aef7c31451abd360019a"},"schema_version":"1.0"},"canonical_sha256":"0f8fa5ee6ad604acad736974b1110dcff9a76b78ef2334ffb2e87414117d7d86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:41.318604Z","signature_b64":"1fQgghiZ4ybamEUChGLOggUq6WZwl7IOcU/R/g8rScV5ByYZ+bCxy4cUmUpoe33aMbbUbKIw5HwxYwFSiVZFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f8fa5ee6ad604acad736974b1110dcff9a76b78ef2334ffb2e87414117d7d86","last_reissued_at":"2026-05-18T00:06:41.318083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:41.318083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.07492","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FqsloUwW6PbYCjJcelLEeE+cU/TphRCh694PTzh2w5Ckg1f+RU72XZ1Emmp+buxmcZTNJ75AccaCiit4B5LrDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T16:37:55.989269Z"},"content_sha256":"1dccead53d24d8501bb08db699e3d4e47357dd0526d62d1c4919b19cbc33ac13","schema_version":"1.0","event_id":"sha256:1dccead53d24d8501bb08db699e3d4e47357dd0526d62d1c4919b19cbc33ac13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B6H2L3TK2YCKZLLTNF2LCEINZ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multilevel estimation of expected exit times and other functionals of stopped diffusions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-fin.CP"],"primary_cat":"math.NA","authors_text":"Francisco Bernal, Michael B. Giles","submitted_at":"2017-10-20T11:30:02Z","abstract_excerpt":"This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexity to achieve an $\\varepsilon$ root-mean-square error is $O(\\varepsilon^{-2}\\, |\\!\\log \\varepsilon|^3)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07492","kind":"arxiv","version":2},"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":"2026-05-18T00:06:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"au90AM12GzDohYmM3mz0UHsDNd2KNf5YusRITUGutkCL3Dn8rBGxK58SIMn0qrSI9n0R1J8/RRFcWNbjCcwYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T16:37:55.989632Z"},"content_sha256":"7fb8770d1ce1d2ebced20845325bc38dadf49f0fdf8fa898b8627afa034c81a0","schema_version":"1.0","event_id":"sha256:7fb8770d1ce1d2ebced20845325bc38dadf49f0fdf8fa898b8627afa034c81a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7/bundle.json","state_url":"https://pith.science/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7/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":"2026-06-21T16:37:55Z","links":{"resolver":"https://pith.science/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7","bundle":"https://pith.science/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7/bundle.json","state":"https://pith.science/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6H2L3TK2YCKZLLTNF2LCEINZ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B6H2L3TK2YCKZLLTNF2LCEINZ7","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":"8f56b1209d8f2c2438ae25544af31bd649d82e7d3797aef7c31451abd360019a","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-20T11:30:02Z","title_canon_sha256":"23ea5244c31a253b9702d04a3d9dcd3ed1a7c52a2a959dfa6d30756a93f41c03"},"schema_version":"1.0","source":{"id":"1710.07492","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.07492","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"arxiv_version","alias_value":"1710.07492v2","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.07492","created_at":"2026-05-18T00:06:41Z"},{"alias_kind":"pith_short_12","alias_value":"B6H2L3TK2YCK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B6H2L3TK2YCKZLLT","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B6H2L3TK","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:7fb8770d1ce1d2ebced20845325bc38dadf49f0fdf8fa898b8627afa034c81a0","target":"graph","created_at":"2026-05-18T00:06:41Z","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":"This paper proposes and analyses a new multilevel Monte Carlo method for the estimation of mean exit times for multi-dimensional Brownian diffusions, and associated functionals which correspond to solutions to high-dimensional parabolic PDEs through the Feynman-Kac formula. In particular, it is proved that the complexity to achieve an $\\varepsilon$ root-mean-square error is $O(\\varepsilon^{-2}\\, |\\!\\log \\varepsilon|^3)$.","authors_text":"Francisco Bernal, Michael B. Giles","cross_cats":["q-fin.CP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-20T11:30:02Z","title":"Multilevel estimation of expected exit times and other functionals of stopped diffusions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.07492","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":"sha256:1dccead53d24d8501bb08db699e3d4e47357dd0526d62d1c4919b19cbc33ac13","target":"record","created_at":"2026-05-18T00:06:41Z","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":"8f56b1209d8f2c2438ae25544af31bd649d82e7d3797aef7c31451abd360019a","cross_cats_sorted":["q-fin.CP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2017-10-20T11:30:02Z","title_canon_sha256":"23ea5244c31a253b9702d04a3d9dcd3ed1a7c52a2a959dfa6d30756a93f41c03"},"schema_version":"1.0","source":{"id":"1710.07492","kind":"arxiv","version":2}},"canonical_sha256":"0f8fa5ee6ad604acad736974b1110dcff9a76b78ef2334ffb2e87414117d7d86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f8fa5ee6ad604acad736974b1110dcff9a76b78ef2334ffb2e87414117d7d86","first_computed_at":"2026-05-18T00:06:41.318083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:41.318083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1fQgghiZ4ybamEUChGLOggUq6WZwl7IOcU/R/g8rScV5ByYZ+bCxy4cUmUpoe33aMbbUbKIw5HwxYwFSiVZFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:41.318604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.07492","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1dccead53d24d8501bb08db699e3d4e47357dd0526d62d1c4919b19cbc33ac13","sha256:7fb8770d1ce1d2ebced20845325bc38dadf49f0fdf8fa898b8627afa034c81a0"],"state_sha256":"13c950e93c54c180a057ecb6cf416183be51b2da7a38095035ad64dbac2bef56"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vYITjfp0Fs7E5FlCQCeHxvXZmODWejxRzHoCeuBZqrmTOyWdbousSW4sLCKpwSIs6pqmGT99B9n3R5A/dvuzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T16:37:55.991577Z","bundle_sha256":"eeff475b6b82d284564d3f333e06c177c933cffabd0c63938966de437fa38cd8"}}