{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:F2RQAFLYBBVQZWSK4EJGZTI3YU","short_pith_number":"pith:F2RQAFLY","schema_version":"1.0","canonical_sha256":"2ea3001578086b0cda4ae1126ccd1bc519918c81337801bb26e1b4f34e00de84","source":{"kind":"arxiv","id":"0704.1796","version":1},"attestation_state":"computed","paper":{"title":"Representation Theorems for Quadratic ${\\cal F}$-Consistent Nonlinear Expectations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jin Ma (Department of Mathematics), Shige Peng (Institute of Mathematics), Song Yao (Department of Mathematics), Ying Hu (IRMAR)","submitted_at":"2007-04-13T17:03:19Z","abstract_excerpt":"In this paper we extend the notion of ``filtration-consistent nonlinear expectation\" (or \"${\\cal F}$-consistent nonlinear expectation\") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental properties of a martingale can still make sense, including the Doob-Meyer type decomposition theorem and the optional sampling theorem. More importantly, we show that any quadratic ${\\cal F}$-consistent nonlinear expectation with a certain domination property must be a quadratic $g$-expectation. Th"},"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":"0704.1796","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"2007-04-13T17:03:19Z","cross_cats_sorted":[],"title_canon_sha256":"69ca9a0931e632637dcb94ffb6fe4299d7e4213c8e08a483305eb32f9de6f3a3","abstract_canon_sha256":"134c31398eada44a6dc7ff165244ab18703d5372a2e02a0d9e9cb9dc1bb6671b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:00:52.638728Z","signature_b64":"EW4c4vXl7EgPRW44XFz060k8PZxRlsfodArR/fLjEicHEyofcEfYW1wZq1kOCPOsGXBo8RoAZgivzrWmmsnaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ea3001578086b0cda4ae1126ccd1bc519918c81337801bb26e1b4f34e00de84","last_reissued_at":"2026-07-04T15:00:52.638392Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:00:52.638392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Representation Theorems for Quadratic ${\\cal F}$-Consistent Nonlinear Expectations","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jin Ma (Department of Mathematics), Shige Peng (Institute of Mathematics), Song Yao (Department of Mathematics), Ying Hu (IRMAR)","submitted_at":"2007-04-13T17:03:19Z","abstract_excerpt":"In this paper we extend the notion of ``filtration-consistent nonlinear expectation\" (or \"${\\cal F}$-consistent nonlinear expectation\") to the case when it is allowed to be dominated by a $g$-expectation that may have a quadratic growth. We show that for such a nonlinear expectation many fundamental properties of a martingale can still make sense, including the Doob-Meyer type decomposition theorem and the optional sampling theorem. More importantly, we show that any quadratic ${\\cal F}$-consistent nonlinear expectation with a certain domination property must be a quadratic $g$-expectation. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0704.1796","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0704.1796/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"0704.1796","created_at":"2026-07-04T15:00:52.638449+00:00"},{"alias_kind":"arxiv_version","alias_value":"0704.1796v1","created_at":"2026-07-04T15:00:52.638449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0704.1796","created_at":"2026-07-04T15:00:52.638449+00:00"},{"alias_kind":"pith_short_12","alias_value":"F2RQAFLYBBVQ","created_at":"2026-07-04T15:00:52.638449+00:00"},{"alias_kind":"pith_short_16","alias_value":"F2RQAFLYBBVQZWSK","created_at":"2026-07-04T15:00:52.638449+00:00"},{"alias_kind":"pith_short_8","alias_value":"F2RQAFLY","created_at":"2026-07-04T15:00:52.638449+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/F2RQAFLYBBVQZWSK4EJGZTI3YU","json":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU.json","graph_json":"https://pith.science/api/pith-number/F2RQAFLYBBVQZWSK4EJGZTI3YU/graph.json","events_json":"https://pith.science/api/pith-number/F2RQAFLYBBVQZWSK4EJGZTI3YU/events.json","paper":"https://pith.science/paper/F2RQAFLY"},"agent_actions":{"view_html":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU","download_json":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU.json","view_paper":"https://pith.science/paper/F2RQAFLY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0704.1796&json=true","fetch_graph":"https://pith.science/api/pith-number/F2RQAFLYBBVQZWSK4EJGZTI3YU/graph.json","fetch_events":"https://pith.science/api/pith-number/F2RQAFLYBBVQZWSK4EJGZTI3YU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU/action/storage_attestation","attest_author":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU/action/author_attestation","sign_citation":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU/action/citation_signature","submit_replication":"https://pith.science/pith/F2RQAFLYBBVQZWSK4EJGZTI3YU/action/replication_record"}},"created_at":"2026-07-04T15:00:52.638449+00:00","updated_at":"2026-07-04T15:00:52.638449+00:00"}