{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:RTT7EKH2YUP53JM4HLOTOD7YCG","short_pith_number":"pith:RTT7EKH2","schema_version":"1.0","canonical_sha256":"8ce7f228fac51fdda59c3add370ff8119b5b33a4c46b48ab9a2a72eca0ff5f67","source":{"kind":"arxiv","id":"1212.2170","version":4},"attestation_state":"computed","paper":{"title":"Stochastic Perron's method for Hamilton-Jacobi-Bellman equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.AP","math.OC"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Mihai Sirbu","submitted_at":"2012-12-10T19:15:33Z","abstract_excerpt":"We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution lying below the value function and a sub-solution dominating it. A comparison argument easily closes the proof. The program has the precise meaning of verification for viscosity-solutions, obtaining the DPP as a conclusion. It also immediately follows that the weak and strong formulations of the stochastic "},"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":"1212.2170","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-12-10T19:15:33Z","cross_cats_sorted":["cs.SY","math.AP","math.OC"],"title_canon_sha256":"e53982701e76f2f5324edc5944a24402438560bac5c28661923c6b103abedb11","abstract_canon_sha256":"4b3a0add2345d2902ef8c097f348ca2d4567db1ac765fa07c6c1858b9a30e92a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:33.169158Z","signature_b64":"JUlPxTuNLcgB1Wroq4r6JsuP2Dk53o/B6q8FM5k5Jdowat8uSOMde+CoAZbWW4fAW/aboAuVHlCDbbhIdkDBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ce7f228fac51fdda59c3add370ff8119b5b33a4c46b48ab9a2a72eca0ff5f67","last_reissued_at":"2026-05-18T03:12:33.168603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:33.168603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stochastic Perron's method for Hamilton-Jacobi-Bellman equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SY","math.AP","math.OC"],"primary_cat":"math.PR","authors_text":"Erhan Bayraktar, Mihai Sirbu","submitted_at":"2012-12-10T19:15:33Z","abstract_excerpt":"We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution lying below the value function and a sub-solution dominating it. A comparison argument easily closes the proof. The program has the precise meaning of verification for viscosity-solutions, obtaining the DPP as a conclusion. It also immediately follows that the weak and strong formulations of the stochastic "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.2170","kind":"arxiv","version":4},"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":"1212.2170","created_at":"2026-05-18T03:12:33.168692+00:00"},{"alias_kind":"arxiv_version","alias_value":"1212.2170v4","created_at":"2026-05-18T03:12:33.168692+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.2170","created_at":"2026-05-18T03:12:33.168692+00:00"},{"alias_kind":"pith_short_12","alias_value":"RTT7EKH2YUP5","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"RTT7EKH2YUP53JM4","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"RTT7EKH2","created_at":"2026-05-18T12:27:20.899486+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/RTT7EKH2YUP53JM4HLOTOD7YCG","json":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG.json","graph_json":"https://pith.science/api/pith-number/RTT7EKH2YUP53JM4HLOTOD7YCG/graph.json","events_json":"https://pith.science/api/pith-number/RTT7EKH2YUP53JM4HLOTOD7YCG/events.json","paper":"https://pith.science/paper/RTT7EKH2"},"agent_actions":{"view_html":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG","download_json":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG.json","view_paper":"https://pith.science/paper/RTT7EKH2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1212.2170&json=true","fetch_graph":"https://pith.science/api/pith-number/RTT7EKH2YUP53JM4HLOTOD7YCG/graph.json","fetch_events":"https://pith.science/api/pith-number/RTT7EKH2YUP53JM4HLOTOD7YCG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG/action/storage_attestation","attest_author":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG/action/author_attestation","sign_citation":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG/action/citation_signature","submit_replication":"https://pith.science/pith/RTT7EKH2YUP53JM4HLOTOD7YCG/action/replication_record"}},"created_at":"2026-05-18T03:12:33.168692+00:00","updated_at":"2026-05-18T03:12:33.168692+00:00"}