{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DVEBEFNVPYGDBEEKMC2BJ6PZZL","short_pith_number":"pith:DVEBEFNV","schema_version":"1.0","canonical_sha256":"1d481215b57e0c30908a60b414f9f9cac3c60131238a311ea8cc581a16d5f45d","source":{"kind":"arxiv","id":"1708.08784","version":1},"attestation_state":"computed","paper":{"title":"Mean-field type Quadratic BSDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"H\\'el\\`ene Hibon (IRMAR), Shanjian Tang (School of Mathematical Sciences), Ying Hu (IRMAR)","submitted_at":"2017-08-28T06:48:48Z","abstract_excerpt":"In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean,"},"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":"1708.08784","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-08-28T06:48:48Z","cross_cats_sorted":[],"title_canon_sha256":"9cb2e276db388b4690f26d8fcb17947fd5ebe64849882a7098cbe501b408eced","abstract_canon_sha256":"54c341498376039eb4ded923656ea842360fdb3c479c7d33bb664937cd5da35f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:25.657941Z","signature_b64":"HsbpgQQE4N0uXJjDOPXF27gGwq+WGQ9cw5WXHnkA2uQdXBwXpD0lEZz4iKqVwh9XlaNJBv/gg/J7vjh62+qyBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1d481215b57e0c30908a60b414f9f9cac3c60131238a311ea8cc581a16d5f45d","last_reissued_at":"2026-05-18T00:36:25.657167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:25.657167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean-field type Quadratic BSDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"H\\'el\\`ene Hibon (IRMAR), Shanjian Tang (School of Mathematical Sciences), Ying Hu (IRMAR)","submitted_at":"2017-08-28T06:48:48Z","abstract_excerpt":"In this paper, we give several new results on solvability of a quadratic BSDE whose generator depends also on the mean of both variables. First, we consider such a BSDE using John-Nirenberg's inequality for BMO martingales to estimate its contribution to the evolution of the first unknown variable. Then we consider the BSDE having an additive expected value of a quadratic generator in addition to the usual quadratic one. In this case, we use a deterministic shift transformation to the first unknown variable, when the usual quadratic generator depends neither on the first variable nor its mean,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08784","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":"1708.08784","created_at":"2026-05-18T00:36:25.657275+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.08784v1","created_at":"2026-05-18T00:36:25.657275+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.08784","created_at":"2026-05-18T00:36:25.657275+00:00"},{"alias_kind":"pith_short_12","alias_value":"DVEBEFNVPYGD","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DVEBEFNVPYGDBEEK","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DVEBEFNV","created_at":"2026-05-18T12:31:12.930513+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/DVEBEFNVPYGDBEEKMC2BJ6PZZL","json":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL.json","graph_json":"https://pith.science/api/pith-number/DVEBEFNVPYGDBEEKMC2BJ6PZZL/graph.json","events_json":"https://pith.science/api/pith-number/DVEBEFNVPYGDBEEKMC2BJ6PZZL/events.json","paper":"https://pith.science/paper/DVEBEFNV"},"agent_actions":{"view_html":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL","download_json":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL.json","view_paper":"https://pith.science/paper/DVEBEFNV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.08784&json=true","fetch_graph":"https://pith.science/api/pith-number/DVEBEFNVPYGDBEEKMC2BJ6PZZL/graph.json","fetch_events":"https://pith.science/api/pith-number/DVEBEFNVPYGDBEEKMC2BJ6PZZL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL/action/storage_attestation","attest_author":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL/action/author_attestation","sign_citation":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL/action/citation_signature","submit_replication":"https://pith.science/pith/DVEBEFNVPYGDBEEKMC2BJ6PZZL/action/replication_record"}},"created_at":"2026-05-18T00:36:25.657275+00:00","updated_at":"2026-05-18T00:36:25.657275+00:00"}