{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:WHTH4JDJRYZ4AK6GV7EYGBS22G","short_pith_number":"pith:WHTH4JDJ","schema_version":"1.0","canonical_sha256":"b1e67e24698e33c02bc6afc983065ad18edb51b94d03eb3a3d4bbd6e7d6b97c8","source":{"kind":"arxiv","id":"1007.2914","version":4},"attestation_state":"computed","paper":{"title":"On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\\^{o} Diffusion and Jump Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Changyong Zhang, Remigijus Mikulevi\\v{c}ius","submitted_at":"2010-07-17T10:01:12Z","abstract_excerpt":"The paper studies the rate of convergence of the weak Euler approximation for It\\^{o} diffusion and jump processes with H\\\"{o}lder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in H\\\"{o}lder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1007.2914","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-17T10:01:12Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"650e4e5f07ca4cdb5ec5345590f33dd1c7bb257147880ccbb36590c609c0b50c","abstract_canon_sha256":"11dd5fba9f766d50786c6edc455d5e8c4a645466230ccf61bc92494c3a1e87b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:47.328773Z","signature_b64":"R6DWYkTKIAuwh1BEvxcmz5/bSSP7b7f5hOhSZh3GUkbIl/mSWH5g5c/vkeVbcx2rz30t7eWw5oUFPei2tZYPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1e67e24698e33c02bc6afc983065ad18edb51b94d03eb3a3d4bbd6e7d6b97c8","last_reissued_at":"2026-05-18T03:02:47.328032Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:47.328032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Rate of Convergence of Weak Euler Approximation for Nondegenerate It\\^{o} Diffusion and Jump Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Changyong Zhang, Remigijus Mikulevi\\v{c}ius","submitted_at":"2010-07-17T10:01:12Z","abstract_excerpt":"The paper studies the rate of convergence of the weak Euler approximation for It\\^{o} diffusion and jump processes with H\\\"{o}lder-continuous generators. It covers a number of stochastic processes including the nondegenerate diffusion processes and a class of stochastic differential equations driven by stable processes. To estimate the rate of convergence, the existence of a unique solution to the corresponding backward Kolmogorov equation in H\\\"{o}lder space is first proved. It then shows that the Euler scheme yields positive weak order of convergence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2914","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1007.2914","created_at":"2026-05-18T03:02:47.328154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1007.2914v4","created_at":"2026-05-18T03:02:47.328154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2914","created_at":"2026-05-18T03:02:47.328154+00:00"},{"alias_kind":"pith_short_12","alias_value":"WHTH4JDJRYZ4","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_16","alias_value":"WHTH4JDJRYZ4AK6G","created_at":"2026-05-18T12:26:15.391820+00:00"},{"alias_kind":"pith_short_8","alias_value":"WHTH4JDJ","created_at":"2026-05-18T12:26:15.391820+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G","json":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G.json","graph_json":"https://pith.science/api/pith-number/WHTH4JDJRYZ4AK6GV7EYGBS22G/graph.json","events_json":"https://pith.science/api/pith-number/WHTH4JDJRYZ4AK6GV7EYGBS22G/events.json","paper":"https://pith.science/paper/WHTH4JDJ"},"agent_actions":{"view_html":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G","download_json":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G.json","view_paper":"https://pith.science/paper/WHTH4JDJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1007.2914&json=true","fetch_graph":"https://pith.science/api/pith-number/WHTH4JDJRYZ4AK6GV7EYGBS22G/graph.json","fetch_events":"https://pith.science/api/pith-number/WHTH4JDJRYZ4AK6GV7EYGBS22G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G/action/storage_attestation","attest_author":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G/action/author_attestation","sign_citation":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G/action/citation_signature","submit_replication":"https://pith.science/pith/WHTH4JDJRYZ4AK6GV7EYGBS22G/action/replication_record"}},"created_at":"2026-05-18T03:02:47.328154+00:00","updated_at":"2026-05-18T03:02:47.328154+00:00"}