{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:NHYBJROVIDAQFYCQ5ISQKP2ZKL","short_pith_number":"pith:NHYBJROV","schema_version":"1.0","canonical_sha256":"69f014c5d540c102e050ea25053f5952ee2f4043f3b02253c969d97daf9262d3","source":{"kind":"arxiv","id":"1803.05182","version":2},"attestation_state":"computed","paper":{"title":"Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.PR","authors_text":"Jingwei Liu","submitted_at":"2018-03-14T09:56:47Z","abstract_excerpt":"The approximative theorems of incomplete Riemann-Stieltjes sums of Ito stochastic integral, mean square integral and Stratonovich stochastic integral with respect to Brownian motion are investigated. Some sufficient conditions of incomplete Riemann-Stieltjes sums approaching stochastic integral are developed, which establish the alternative ways to converge stochastic integral. And, Two simulation examples of incomplete Riemann-Stieltjes sums about Ito stochastic integral and Stratonovich stochastic integral are given for demonstration."},"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":"1803.05182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-14T09:56:47Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2837f9aa140802696d0b83cfedff05b5d5eb2312678c413213a7410f1f3c4348","abstract_canon_sha256":"c330c2578fe787c45847940d158c69b01a5ebec1bbdf467bdad3e0d14a84145f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:53.296268Z","signature_b64":"zDW4oGbyduq25SijxOhbZ1cOROHbQvFMQl/o+eAxvWE+8AZldZiONnTVCOOf8AiRBNaIOTnR28PWFDQdIDAdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"69f014c5d540c102e050ea25053f5952ee2f4043f3b02253c969d97daf9262d3","last_reissued_at":"2026-05-17T23:52:53.294762Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:53.294762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximative Theorem of Incomplete Riemann-Stieltjes Sum of Stochastic Integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.PR","authors_text":"Jingwei Liu","submitted_at":"2018-03-14T09:56:47Z","abstract_excerpt":"The approximative theorems of incomplete Riemann-Stieltjes sums of Ito stochastic integral, mean square integral and Stratonovich stochastic integral with respect to Brownian motion are investigated. Some sufficient conditions of incomplete Riemann-Stieltjes sums approaching stochastic integral are developed, which establish the alternative ways to converge stochastic integral. And, Two simulation examples of incomplete Riemann-Stieltjes sums about Ito stochastic integral and Stratonovich stochastic integral are given for demonstration."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05182","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1803.05182","created_at":"2026-05-17T23:52:53.294924+00:00"},{"alias_kind":"arxiv_version","alias_value":"1803.05182v2","created_at":"2026-05-17T23:52:53.294924+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05182","created_at":"2026-05-17T23:52:53.294924+00:00"},{"alias_kind":"pith_short_12","alias_value":"NHYBJROVIDAQ","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"NHYBJROVIDAQFYCQ","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"NHYBJROV","created_at":"2026-05-18T12:32:40.477152+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/NHYBJROVIDAQFYCQ5ISQKP2ZKL","json":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL.json","graph_json":"https://pith.science/api/pith-number/NHYBJROVIDAQFYCQ5ISQKP2ZKL/graph.json","events_json":"https://pith.science/api/pith-number/NHYBJROVIDAQFYCQ5ISQKP2ZKL/events.json","paper":"https://pith.science/paper/NHYBJROV"},"agent_actions":{"view_html":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL","download_json":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL.json","view_paper":"https://pith.science/paper/NHYBJROV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1803.05182&json=true","fetch_graph":"https://pith.science/api/pith-number/NHYBJROVIDAQFYCQ5ISQKP2ZKL/graph.json","fetch_events":"https://pith.science/api/pith-number/NHYBJROVIDAQFYCQ5ISQKP2ZKL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL/action/storage_attestation","attest_author":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL/action/author_attestation","sign_citation":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL/action/citation_signature","submit_replication":"https://pith.science/pith/NHYBJROVIDAQFYCQ5ISQKP2ZKL/action/replication_record"}},"created_at":"2026-05-17T23:52:53.294924+00:00","updated_at":"2026-05-17T23:52:53.294924+00:00"}