{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4VY2725XECKQ7MKY5XSDQWBDXJ","short_pith_number":"pith:4VY2725X","canonical_record":{"source":{"id":"1203.5809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-26T20:32:29Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"493108d7ca5208fdbb04985b905e5b5cc9514425577e96c0f2138b3a0a72f27e","abstract_canon_sha256":"aec484a1eddd380babe1f7195a7802f35df3e87d12fc60d1983e66f416053d46"},"schema_version":"1.0"},"canonical_sha256":"e571afebb720950fb158ede4385823ba627d6154c90f4352308f51a4d093900b","source":{"kind":"arxiv","id":"1203.5809","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5809","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5809v2","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5809","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"4VY2725XECKQ","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"pith_short_16","alias_value":"4VY2725XECKQ7MKY","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"pith_short_8","alias_value":"4VY2725X","created_at":"2026-06-03T23:07:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4VY2725XECKQ7MKY5XSDQWBDXJ","target":"record","payload":{"canonical_record":{"source":{"id":"1203.5809","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-26T20:32:29Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"493108d7ca5208fdbb04985b905e5b5cc9514425577e96c0f2138b3a0a72f27e","abstract_canon_sha256":"aec484a1eddd380babe1f7195a7802f35df3e87d12fc60d1983e66f416053d46"},"schema_version":"1.0"},"canonical_sha256":"e571afebb720950fb158ede4385823ba627d6154c90f4352308f51a4d093900b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-03T23:07:16.211295Z","signature_b64":"E3k5GyCQNOjKvnCThifWnS1+JG4DeiS4BRHNVdbCWUygDxl19tO7s6OhzKuen/dqGtsCZA3PWeyzyn+rhWs2Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e571afebb720950fb158ede4385823ba627d6154c90f4352308f51a4d093900b","last_reissued_at":"2026-06-03T23:07:16.210792Z","signature_status":"signed_v1","first_computed_at":"2026-06-03T23:07:16.210792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1203.5809","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":"2026-06-03T23:07:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QskpXTi5hBT9OCfVIQV5qXsljIwpVaapANVWzSojtQ30WH62n6MemSgzgQxCB1iFOjTwW7vZh/2OtSeg+xaDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:25:33.810040Z"},"content_sha256":"19c021af07d8b47b50ff4db775f2ebfbe50e3056d12d38c920f3e5f1d567c644","schema_version":"1.0","event_id":"sha256:19c021af07d8b47b50ff4db775f2ebfbe50e3056d12d38c920f3e5f1d567c644"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4VY2725XECKQ7MKY5XSDQWBDXJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"math.PR","authors_text":"Arnulf Jentzen, Martin Hutzenthaler","submitted_at":"2012-03-26T20:32:29Z","abstract_excerpt":"Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, we establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5809","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1203.5809/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-03T23:07:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KpRgFXzt97W5klN7m68vD6uv0ayfOQWnolTRFzfmMu6JYWdbt1e3A2qYCHWwV0N4URoe54u4OAO5vg5w8M1PCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:25:33.810436Z"},"content_sha256":"b665b64b474993edae4ed8707c04ba73d7e8bb7efabf12ad943c5e0d3998ff99","schema_version":"1.0","event_id":"sha256:b665b64b474993edae4ed8707c04ba73d7e8bb7efabf12ad943c5e0d3998ff99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4VY2725XECKQ7MKY5XSDQWBDXJ/bundle.json","state_url":"https://pith.science/pith/4VY2725XECKQ7MKY5XSDQWBDXJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4VY2725XECKQ7MKY5XSDQWBDXJ/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":"2026-06-22T23:25:33Z","links":{"resolver":"https://pith.science/pith/4VY2725XECKQ7MKY5XSDQWBDXJ","bundle":"https://pith.science/pith/4VY2725XECKQ7MKY5XSDQWBDXJ/bundle.json","state":"https://pith.science/pith/4VY2725XECKQ7MKY5XSDQWBDXJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4VY2725XECKQ7MKY5XSDQWBDXJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4VY2725XECKQ7MKY5XSDQWBDXJ","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":"aec484a1eddd380babe1f7195a7802f35df3e87d12fc60d1983e66f416053d46","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-26T20:32:29Z","title_canon_sha256":"493108d7ca5208fdbb04985b905e5b5cc9514425577e96c0f2138b3a0a72f27e"},"schema_version":"1.0","source":{"id":"1203.5809","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.5809","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"arxiv_version","alias_value":"1203.5809v2","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5809","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"pith_short_12","alias_value":"4VY2725XECKQ","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"pith_short_16","alias_value":"4VY2725XECKQ7MKY","created_at":"2026-06-03T23:07:16Z"},{"alias_kind":"pith_short_8","alias_value":"4VY2725X","created_at":"2026-06-03T23:07:16Z"}],"graph_snapshots":[{"event_id":"sha256:b665b64b474993edae4ed8707c04ba73d7e8bb7efabf12ad943c5e0d3998ff99","target":"graph","created_at":"2026-06-03T23:07:16Z","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/1203.5809/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, we establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which r","authors_text":"Arnulf Jentzen, Martin Hutzenthaler","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-26T20:32:29Z","title":"Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5809","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":"sha256:19c021af07d8b47b50ff4db775f2ebfbe50e3056d12d38c920f3e5f1d567c644","target":"record","created_at":"2026-06-03T23:07:16Z","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":"aec484a1eddd380babe1f7195a7802f35df3e87d12fc60d1983e66f416053d46","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-26T20:32:29Z","title_canon_sha256":"493108d7ca5208fdbb04985b905e5b5cc9514425577e96c0f2138b3a0a72f27e"},"schema_version":"1.0","source":{"id":"1203.5809","kind":"arxiv","version":2}},"canonical_sha256":"e571afebb720950fb158ede4385823ba627d6154c90f4352308f51a4d093900b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e571afebb720950fb158ede4385823ba627d6154c90f4352308f51a4d093900b","first_computed_at":"2026-06-03T23:07:16.210792Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T23:07:16.210792Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"E3k5GyCQNOjKvnCThifWnS1+JG4DeiS4BRHNVdbCWUygDxl19tO7s6OhzKuen/dqGtsCZA3PWeyzyn+rhWs2Bw==","signature_status":"signed_v1","signed_at":"2026-06-03T23:07:16.211295Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.5809","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19c021af07d8b47b50ff4db775f2ebfbe50e3056d12d38c920f3e5f1d567c644","sha256:b665b64b474993edae4ed8707c04ba73d7e8bb7efabf12ad943c5e0d3998ff99"],"state_sha256":"78db11d945092fb137082090fe45f6031967c62251e006db1bf516235ee42524"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTgtM4Xj3v4siQg1bYeRvDXWevbtyhf0k0X+Ipq6Oqnrh2Jhh8S7VYW+fiJqUVIuL2CwfZrwEAG9iBNiVVPKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:25:33.812521Z","bundle_sha256":"cfc15b9b24c5ec7b9fbd4d271ea577322289e0118fb5ab10a3bd7327e65b6e7f"}}