{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YHU5UYFKO2NEUA4GLM3MQLNBC4","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":"4f620862361dc10bc6dfb415c99aa8f475f1e279b76143e425cccc94484a6696","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-21T18:47:38Z","title_canon_sha256":"07a02357cd6546d876836929c172e6dd7b147ba2420cfbe9578d4b97a3362fad"},"schema_version":"1.0","source":{"id":"1712.08152","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.08152","created_at":"2026-05-17T23:42:03Z"},{"alias_kind":"arxiv_version","alias_value":"1712.08152v2","created_at":"2026-05-17T23:42:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08152","created_at":"2026-05-17T23:42:03Z"},{"alias_kind":"pith_short_12","alias_value":"YHU5UYFKO2NE","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YHU5UYFKO2NEUA4G","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YHU5UYFK","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:1b8b8a86ed395938eea37d17fdfa3989c8b327bf83d4f08dcfb6011454c06b94","target":"graph","created_at":"2026-05-17T23:42:03Z","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 study the numerical quadrature of a stochastic integral, where the temporal regularity of the integrand is measured in the fractional Sobolev-Slobodeckij norm in $W^{\\sigma,p}(0,T)$, $\\sigma \\in (0,2)$, $p \\in [2,\\infty)$. We introduce two quadrature rules: The first is best suited for the parameter range $\\sigma \\in (0,1)$ and consists of a Riemann-Maruyama approximation on a randomly shifted grid. The second quadrature rule considered in this paper applies to the case of a deterministic integrand of fractional Sobolev regularity with $\\sigma \\in (1,2)$. In both cases the ord","authors_text":"Monika Eisenmann, Raphael Kruse","cross_cats":["math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-21T18:47:38Z","title":"Two quadrature rules for stochastic It\\^o-integrals with fractional Sobolev regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08152","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":"sha256:4d101545a621c318d6def573d101be7d41f517516c004c2343df4a52a0f51a8a","target":"record","created_at":"2026-05-17T23:42:03Z","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":"4f620862361dc10bc6dfb415c99aa8f475f1e279b76143e425cccc94484a6696","cross_cats_sorted":["math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-21T18:47:38Z","title_canon_sha256":"07a02357cd6546d876836929c172e6dd7b147ba2420cfbe9578d4b97a3362fad"},"schema_version":"1.0","source":{"id":"1712.08152","kind":"arxiv","version":2}},"canonical_sha256":"c1e9da60aa769a4a03865b36c82da1171b554f3fd5da6fabcab6c4092cfde119","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c1e9da60aa769a4a03865b36c82da1171b554f3fd5da6fabcab6c4092cfde119","first_computed_at":"2026-05-17T23:42:03.326455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:03.326455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UQR08Mg0pyCx/4ale2OSniN21KFSMsy44tuJmp8BzLHarkehVZo79KCDH3VtiQo0U7tGY9DLS+Sbq9hhG2UzAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:03.327199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.08152","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d101545a621c318d6def573d101be7d41f517516c004c2343df4a52a0f51a8a","sha256:1b8b8a86ed395938eea37d17fdfa3989c8b327bf83d4f08dcfb6011454c06b94"],"state_sha256":"bf8f07eb32ef9482faef083f19f211e0a236f02cbf704ab04a0460691216d47b"}