{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:YIOG73C5B2P66TFI5DPH3DRE2F","short_pith_number":"pith:YIOG73C5","canonical_record":{"source":{"id":"1811.07832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-19T17:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"7d22dccad255ecacee0e8db772d49ba047b29dda820298ac548e33c785e3f430","abstract_canon_sha256":"55db5e9c13108385e48e8d28b49852a3c734d4ed932bd4abadc54ed6e514e176"},"schema_version":"1.0"},"canonical_sha256":"c21c6fec5d0e9fef4ca8e8de7d8e24d165dfce87e7675d6ace92bd46147c88aa","source":{"kind":"arxiv","id":"1811.07832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07832","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07832v1","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07832","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"YIOG73C5B2P6","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YIOG73C5B2P66TFI","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YIOG73C5","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:YIOG73C5B2P66TFI5DPH3DRE2F","target":"record","payload":{"canonical_record":{"source":{"id":"1811.07832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-19T17:44:34Z","cross_cats_sorted":[],"title_canon_sha256":"7d22dccad255ecacee0e8db772d49ba047b29dda820298ac548e33c785e3f430","abstract_canon_sha256":"55db5e9c13108385e48e8d28b49852a3c734d4ed932bd4abadc54ed6e514e176"},"schema_version":"1.0"},"canonical_sha256":"c21c6fec5d0e9fef4ca8e8de7d8e24d165dfce87e7675d6ace92bd46147c88aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:23.363516Z","signature_b64":"vCgduff4PG18aIrbbxCRmeCFzuWZtUq1te/a4mbf12nKUpEoO3PxeH0st9oB5zKBEYJczlzfFPYaaI3LIEDhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c21c6fec5d0e9fef4ca8e8de7d8e24d165dfce87e7675d6ace92bd46147c88aa","last_reissued_at":"2026-05-18T00:00:23.363009Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:23.363009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.07832","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":"2026-05-18T00:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8n1CIfLttJERBGE5BJ5VyVqh5YKof//rMf+5vzhVRT4/EN1Zgt2TlMSFCi/crm+qr7fInGYgJvzec2EXQLBkAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:13:31.127070Z"},"content_sha256":"294d3675049f52b1e298d0424680a17a39e74ba7a716cf53a302532ebc62a06b","schema_version":"1.0","event_id":"sha256:294d3675049f52b1e298d0424680a17a39e74ba7a716cf53a302532ebc62a06b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:YIOG73C5B2P66TFI5DPH3DRE2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Edgeworth expansion for Euler approximation of continuous diffusion processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bezirgen Veliyev, Mark Podolskij, nakahiro yoshida","submitted_at":"2018-11-19T17:44:34Z","abstract_excerpt":"In this paper we present the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work \\cite{Yoshida2013}, which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to the Euler scheme, and for studentized version of the error process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07832","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":"2026-05-18T00:00:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OXe6TrD2wNhbh/EnSTZKYrEZZIiPGZgFnZsyccNAhHz3ylfGR1hGW3Eup9IcW9kgRhRXoL/EsaPEIWimT7xaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T01:13:31.127717Z"},"content_sha256":"5302501c13d4fd1544ee77cf0aa3a33641baf6e2f429617df820239242062eb8","schema_version":"1.0","event_id":"sha256:5302501c13d4fd1544ee77cf0aa3a33641baf6e2f429617df820239242062eb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YIOG73C5B2P66TFI5DPH3DRE2F/bundle.json","state_url":"https://pith.science/pith/YIOG73C5B2P66TFI5DPH3DRE2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YIOG73C5B2P66TFI5DPH3DRE2F/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":"2026-05-31T01:13:31Z","links":{"resolver":"https://pith.science/pith/YIOG73C5B2P66TFI5DPH3DRE2F","bundle":"https://pith.science/pith/YIOG73C5B2P66TFI5DPH3DRE2F/bundle.json","state":"https://pith.science/pith/YIOG73C5B2P66TFI5DPH3DRE2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YIOG73C5B2P66TFI5DPH3DRE2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:YIOG73C5B2P66TFI5DPH3DRE2F","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":"55db5e9c13108385e48e8d28b49852a3c734d4ed932bd4abadc54ed6e514e176","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-19T17:44:34Z","title_canon_sha256":"7d22dccad255ecacee0e8db772d49ba047b29dda820298ac548e33c785e3f430"},"schema_version":"1.0","source":{"id":"1811.07832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07832","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07832v1","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07832","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"YIOG73C5B2P6","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"YIOG73C5B2P66TFI","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"YIOG73C5","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:5302501c13d4fd1544ee77cf0aa3a33641baf6e2f429617df820239242062eb8","target":"graph","created_at":"2026-05-18T00:00:23Z","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 the Edgeworth expansion for the Euler approximation scheme of a continuous diffusion process driven by a Brownian motion. Our methodology is based upon a recent work \\cite{Yoshida2013}, which establishes Edgeworth expansions associated with asymptotic mixed normality using elements of Malliavin calculus. Potential applications of our theoretical results include higher order expansions for weak and strong approximation errors associated to the Euler scheme, and for studentized version of the error process.","authors_text":"Bezirgen Veliyev, Mark Podolskij, nakahiro yoshida","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-19T17:44:34Z","title":"Edgeworth expansion for Euler approximation of continuous diffusion processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07832","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":"sha256:294d3675049f52b1e298d0424680a17a39e74ba7a716cf53a302532ebc62a06b","target":"record","created_at":"2026-05-18T00:00:23Z","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":"55db5e9c13108385e48e8d28b49852a3c734d4ed932bd4abadc54ed6e514e176","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-19T17:44:34Z","title_canon_sha256":"7d22dccad255ecacee0e8db772d49ba047b29dda820298ac548e33c785e3f430"},"schema_version":"1.0","source":{"id":"1811.07832","kind":"arxiv","version":1}},"canonical_sha256":"c21c6fec5d0e9fef4ca8e8de7d8e24d165dfce87e7675d6ace92bd46147c88aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c21c6fec5d0e9fef4ca8e8de7d8e24d165dfce87e7675d6ace92bd46147c88aa","first_computed_at":"2026-05-18T00:00:23.363009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:23.363009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vCgduff4PG18aIrbbxCRmeCFzuWZtUq1te/a4mbf12nKUpEoO3PxeH0st9oB5zKBEYJczlzfFPYaaI3LIEDhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:23.363516Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:294d3675049f52b1e298d0424680a17a39e74ba7a716cf53a302532ebc62a06b","sha256:5302501c13d4fd1544ee77cf0aa3a33641baf6e2f429617df820239242062eb8"],"state_sha256":"ef047777ce3dfee08f56990ce20662f3968b36c1491939f30888c7bfa34dac11"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dT42+A4Ec467hY7VVmYoJJ0arR8KUfcIEq1y/uZLdkay8ZUx6K8ZfFdnAXjZqM3LEDsxzwmN+PxEroDV0O/JBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T01:13:31.130386Z","bundle_sha256":"7a33d2be2d7bea32491df92cc5600f5e2a3044dbd9992f9e5656ba48182426d1"}}