{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:PEZ5YSITMZPAPD4VFLIYGLTE4P","short_pith_number":"pith:PEZ5YSIT","schema_version":"1.0","canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","source":{"kind":"arxiv","id":"1704.05212","version":1},"attestation_state":"computed","paper":{"title":"Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shanjian Tang (School of Mathematical Sciences), Ying Hu (IRMAR)","submitted_at":"2017-04-18T06:32:24Z","abstract_excerpt":"In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some $\\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\\log L$ integrability.  We show by a counterexample that $L\\log L$ integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator."},"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":"1704.05212","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-18T06:32:24Z","cross_cats_sorted":[],"title_canon_sha256":"1c0155e566767e9c52f60d3c361e97f80ec6933af9756cfe65b1f941b9766190","abstract_canon_sha256":"6715ca35b2a45f2d1e4bf88c9be1cd8a9787d74da11c952a83d57b48897862e3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:11.513508Z","signature_b64":"gGRmWzfVBpjTVD89LFT08h2Nkl1/5vI73PKY07He+a1LhbXqzF3W2lTZ/hFk0+CAaDyUOYL+gvVVWlSBgBK7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7933dc4913665e078f952ad1832e64e3fe918db05fc4b3a949819266aae856b3","last_reissued_at":"2026-05-18T00:46:11.513062Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:11.513062Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Existence of solution to scalar BSDEs with weakly $L^{1+}$-integrable terminal values","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Shanjian Tang (School of Mathematical Sciences), Ying Hu (IRMAR)","submitted_at":"2017-04-18T06:32:24Z","abstract_excerpt":"In this paper, we study a scalar linearly growing BSDE with a weakly $L^{1+}$-integrable terminal value. We prove that the BSDE admits a solutionif the terminal value satisfies some $\\Psi$-integrability condition, which is weaker than the usual $L^p$ ($p>1$) integrability and stronger than $L\\log L$ integrability.  We show by a counterexample that $L\\log L$ integrability is not sufficient for the existence of solutionto a BSDE of a linearly growing generator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05212","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1704.05212","created_at":"2026-05-18T00:46:11.513131+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.05212v1","created_at":"2026-05-18T00:46:11.513131+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05212","created_at":"2026-05-18T00:46:11.513131+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEZ5YSITMZPA","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEZ5YSITMZPAPD4V","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEZ5YSIT","created_at":"2026-05-18T12:31:37.085036+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/PEZ5YSITMZPAPD4VFLIYGLTE4P","json":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P.json","graph_json":"https://pith.science/api/pith-number/PEZ5YSITMZPAPD4VFLIYGLTE4P/graph.json","events_json":"https://pith.science/api/pith-number/PEZ5YSITMZPAPD4VFLIYGLTE4P/events.json","paper":"https://pith.science/paper/PEZ5YSIT"},"agent_actions":{"view_html":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P","download_json":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P.json","view_paper":"https://pith.science/paper/PEZ5YSIT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.05212&json=true","fetch_graph":"https://pith.science/api/pith-number/PEZ5YSITMZPAPD4VFLIYGLTE4P/graph.json","fetch_events":"https://pith.science/api/pith-number/PEZ5YSITMZPAPD4VFLIYGLTE4P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/action/storage_attestation","attest_author":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/action/author_attestation","sign_citation":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/action/citation_signature","submit_replication":"https://pith.science/pith/PEZ5YSITMZPAPD4VFLIYGLTE4P/action/replication_record"}},"created_at":"2026-05-18T00:46:11.513131+00:00","updated_at":"2026-05-18T00:46:11.513131+00:00"}