{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:AXZJ5KRMWJ7QMVQGP72GNN3I2K","short_pith_number":"pith:AXZJ5KRM","canonical_record":{"source":{"id":"1309.1839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-07T08:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"0571ec9c2f7186cf7b8b83d8717592bc7848a58a68ba88a5ed5aa0eb7f9824e3","abstract_canon_sha256":"1557e2451962ef9a31534afacc06f4bc337b0c4201127a0b28626cea82ec6ffb"},"schema_version":"1.0"},"canonical_sha256":"05f29eaa2cb27f0656067ff466b768d2a1246d31adf51dcfdebbb030d14bba0d","source":{"kind":"arxiv","id":"1309.1839","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1839","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1839v1","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1839","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"AXZJ5KRMWJ7Q","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AXZJ5KRMWJ7QMVQG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AXZJ5KRM","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:AXZJ5KRMWJ7QMVQGP72GNN3I2K","target":"record","payload":{"canonical_record":{"source":{"id":"1309.1839","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-07T08:30:03Z","cross_cats_sorted":[],"title_canon_sha256":"0571ec9c2f7186cf7b8b83d8717592bc7848a58a68ba88a5ed5aa0eb7f9824e3","abstract_canon_sha256":"1557e2451962ef9a31534afacc06f4bc337b0c4201127a0b28626cea82ec6ffb"},"schema_version":"1.0"},"canonical_sha256":"05f29eaa2cb27f0656067ff466b768d2a1246d31adf51dcfdebbb030d14bba0d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:57.337693Z","signature_b64":"r2m8+SDVENBD6iBTMcWeCepKjgkgig13W0/hwCWxTPqejpP5c2VSgI/fu96pMduPWUtNFt49dwxnDtH1NlMwDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05f29eaa2cb27f0656067ff466b768d2a1246d31adf51dcfdebbb030d14bba0d","last_reissued_at":"2026-05-18T03:13:57.336996Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:57.336996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.1839","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TDQok/5W5uyS3KxaFpwrusaQ785YEO/lUQ/XFTVZa+58MjFy6c2fQorC7Z5Uag4ILwrkXu0UlaGiYIUmanBMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:36:41.978729Z"},"content_sha256":"fcb0dd6a5b9e766c00678bb89e64d8f73a2013648f9efbf88a5a031e5fb9c211","schema_version":"1.0","event_id":"sha256:fcb0dd6a5b9e766c00678bb89e64d8f73a2013648f9efbf88a5a031e5fb9c211"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:AXZJ5KRMWJ7QMVQGP72GNN3I2K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An Euler-Poisson Scheme for L\\'evy driven SDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Albert Ferreiro-Castilla, Andreas E Kyprianou, Robert Scheichl","submitted_at":"2013-09-07T08:30:03Z","abstract_excerpt":"We describe an Euler scheme to approximate solutions of L\\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the authors in Ferreiro-Castilla et al. (2012). We provide a complete numerical analysis of the algorithm to approximate the terminal value of the SDE and proof that the approximation converges in mean square error with rate $\\mathcal{O}(n^{-1/2})$. The only requirement of the methodology is to have exact samples from the resolvent of the L\\'evy process driving t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1839","kind":"arxiv","version":1},"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":"2026-05-18T03:13:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+NJ3I+2Rsisdp/YB+hxnIdtP7unBQbkNN5cnPg78q2T/pn0CEAS9Gw3durm+SHIMYKyJjdAFUhmJTmFPBc4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T19:36:41.979073Z"},"content_sha256":"06660d5c6fb30e09acf74aa0efbe89fd75e6542b193084a5a0d9ba7e1189aa9e","schema_version":"1.0","event_id":"sha256:06660d5c6fb30e09acf74aa0efbe89fd75e6542b193084a5a0d9ba7e1189aa9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K/bundle.json","state_url":"https://pith.science/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K/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":"2026-06-23T19:36:41Z","links":{"resolver":"https://pith.science/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K","bundle":"https://pith.science/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K/bundle.json","state":"https://pith.science/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXZJ5KRMWJ7QMVQGP72GNN3I2K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:AXZJ5KRMWJ7QMVQGP72GNN3I2K","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":"1557e2451962ef9a31534afacc06f4bc337b0c4201127a0b28626cea82ec6ffb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-07T08:30:03Z","title_canon_sha256":"0571ec9c2f7186cf7b8b83d8717592bc7848a58a68ba88a5ed5aa0eb7f9824e3"},"schema_version":"1.0","source":{"id":"1309.1839","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.1839","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"arxiv_version","alias_value":"1309.1839v1","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.1839","created_at":"2026-05-18T03:13:57Z"},{"alias_kind":"pith_short_12","alias_value":"AXZJ5KRMWJ7Q","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"AXZJ5KRMWJ7QMVQG","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"AXZJ5KRM","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:06660d5c6fb30e09acf74aa0efbe89fd75e6542b193084a5a0d9ba7e1189aa9e","target":"graph","created_at":"2026-05-18T03:13:57Z","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 describe an Euler scheme to approximate solutions of L\\'evy driven Stochastic Differential Equations (SDE) where the grid points are random and given by the arrival times of a Poisson process. This result extends a previous work of the authors in Ferreiro-Castilla et al. (2012). We provide a complete numerical analysis of the algorithm to approximate the terminal value of the SDE and proof that the approximation converges in mean square error with rate $\\mathcal{O}(n^{-1/2})$. The only requirement of the methodology is to have exact samples from the resolvent of the L\\'evy process driving t","authors_text":"Albert Ferreiro-Castilla, Andreas E Kyprianou, Robert Scheichl","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-07T08:30:03Z","title":"An Euler-Poisson Scheme for L\\'evy driven SDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.1839","kind":"arxiv","version":1},"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:fcb0dd6a5b9e766c00678bb89e64d8f73a2013648f9efbf88a5a031e5fb9c211","target":"record","created_at":"2026-05-18T03:13:57Z","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":"1557e2451962ef9a31534afacc06f4bc337b0c4201127a0b28626cea82ec6ffb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-07T08:30:03Z","title_canon_sha256":"0571ec9c2f7186cf7b8b83d8717592bc7848a58a68ba88a5ed5aa0eb7f9824e3"},"schema_version":"1.0","source":{"id":"1309.1839","kind":"arxiv","version":1}},"canonical_sha256":"05f29eaa2cb27f0656067ff466b768d2a1246d31adf51dcfdebbb030d14bba0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05f29eaa2cb27f0656067ff466b768d2a1246d31adf51dcfdebbb030d14bba0d","first_computed_at":"2026-05-18T03:13:57.336996Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:57.336996Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r2m8+SDVENBD6iBTMcWeCepKjgkgig13W0/hwCWxTPqejpP5c2VSgI/fu96pMduPWUtNFt49dwxnDtH1NlMwDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:57.337693Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.1839","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcb0dd6a5b9e766c00678bb89e64d8f73a2013648f9efbf88a5a031e5fb9c211","sha256:06660d5c6fb30e09acf74aa0efbe89fd75e6542b193084a5a0d9ba7e1189aa9e"],"state_sha256":"c9feb8211e7b530803f7217e04aefb2fcb1b00a50948c8d24719d4a25476f1cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k6763QegeQTmUTObAPOXKGRC+WNdTFvneUB4nQQwj0o5aWdzQr6QREj0FZ4rbOMxFZHQ83ESUmnRwpaoGoERDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T19:36:41.981005Z","bundle_sha256":"c865531abfcb037549b6b64427e14e89b9bc343f6512c15bd24ec035b89fd3af"}}