{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ETV6O7BR36BFNCM6JPLDULG75J","short_pith_number":"pith:ETV6O7BR","schema_version":"1.0","canonical_sha256":"24ebe77c31df8256899e4bd63a2cdfea599aca5f2b024e403af53ef25c92d9ef","source":{"kind":"arxiv","id":"1701.03870","version":1},"attestation_state":"computed","paper":{"title":"A representation theorem for generators of BSDEs with general growth generators in $y$ and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lishun Xiao, ShengJun Fan","submitted_at":"2017-01-14T02:13:49Z","abstract_excerpt":"In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques, where the generators only need to satisfy a weak monotonicity condition and a general growth condition in $y$ and a Lipschitz condition in $z$. This result basically solves the problem of representation theorems for generators of BSDEs with general growth generators in $y$. Then, such representation theorem is adopted to prove a probabilistic formula, in vis"},"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":"1701.03870","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-01-14T02:13:49Z","cross_cats_sorted":[],"title_canon_sha256":"be846f1faa753c7eaeee9e392a840f2d5a5eb59cfe57af18dd8615e05f2d232a","abstract_canon_sha256":"3921e359b05cd7595d13ee51cad222e76dc159efec03951b04f83e2992725229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:48.683360Z","signature_b64":"KP818DxaLlTLhJFaG8jWLpfVnWfqbU/CI6AIexk4jxNQMZo9GfhVIgffYkR8WTo1JjnRGXfUmy0+pvYr/y32BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24ebe77c31df8256899e4bd63a2cdfea599aca5f2b024e403af53ef25c92d9ef","last_reissued_at":"2026-05-18T00:52:48.682613Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:48.682613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A representation theorem for generators of BSDEs with general growth generators in $y$ and its applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lishun Xiao, ShengJun Fan","submitted_at":"2017-01-14T02:13:49Z","abstract_excerpt":"In this paper we first prove a general representation theorem for generators of backward stochastic differential equations (BSDEs for short) by utilizing a localization method involved with stopping time tools and approximation techniques, where the generators only need to satisfy a weak monotonicity condition and a general growth condition in $y$ and a Lipschitz condition in $z$. This result basically solves the problem of representation theorems for generators of BSDEs with general growth generators in $y$. Then, such representation theorem is adopted to prove a probabilistic formula, in vis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03870","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":"1701.03870","created_at":"2026-05-18T00:52:48.682736+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.03870v1","created_at":"2026-05-18T00:52:48.682736+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03870","created_at":"2026-05-18T00:52:48.682736+00:00"},{"alias_kind":"pith_short_12","alias_value":"ETV6O7BR36BF","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"ETV6O7BR36BFNCM6","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"ETV6O7BR","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/ETV6O7BR36BFNCM6JPLDULG75J","json":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J.json","graph_json":"https://pith.science/api/pith-number/ETV6O7BR36BFNCM6JPLDULG75J/graph.json","events_json":"https://pith.science/api/pith-number/ETV6O7BR36BFNCM6JPLDULG75J/events.json","paper":"https://pith.science/paper/ETV6O7BR"},"agent_actions":{"view_html":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J","download_json":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J.json","view_paper":"https://pith.science/paper/ETV6O7BR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.03870&json=true","fetch_graph":"https://pith.science/api/pith-number/ETV6O7BR36BFNCM6JPLDULG75J/graph.json","fetch_events":"https://pith.science/api/pith-number/ETV6O7BR36BFNCM6JPLDULG75J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J/action/storage_attestation","attest_author":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J/action/author_attestation","sign_citation":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J/action/citation_signature","submit_replication":"https://pith.science/pith/ETV6O7BR36BFNCM6JPLDULG75J/action/replication_record"}},"created_at":"2026-05-18T00:52:48.682736+00:00","updated_at":"2026-05-18T00:52:48.682736+00:00"}