{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TMNGP2GKWLYFDOQV66GXUE3FM6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"20c301c509fd3e0f6cbd30e8912bbb26eb4e07392a72e4d7b662dbbb59811c49","cross_cats_sorted":["cs.SY","math.OC","q-fin.RM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-16T17:00:11Z","title_canon_sha256":"acc8a677c330d9c348daca2ad9834cf824ebd4c27ffaf452458bbbf383502923"},"schema_version":"1.0","source":{"id":"1106.3273","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.3273","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"1106.3273v2","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.3273","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"TMNGP2GKWLYF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TMNGP2GKWLYFDOQV","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TMNGP2GK","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:28fb737669f5624f18521c609080489e9ebbcd888902f7f77e4fc77540cd5a81","target":"graph","created_at":"2026-05-18T03:56:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular measures, rather than the usual family of processes indexed by the controls. This value process is characterized by a second order backward SDE, which can be seen as a non-Markovian analogue of the Hamilton-Jacobi-Bellman partial differential equation. Moreover, our value process yields a generalization of the G-expectation to the context of SDEs.","authors_text":"Marcel Nutz","cross_cats":["cs.SY","math.OC","q-fin.RM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-16T17:00:11Z","title":"A Quasi-Sure Approach to the Control of Non-Markovian Stochastic Differential Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.3273","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c5e9bf6fb9ad6dcff8ffeab04902110b7c78d8a00510ee8d57110dd70fb214a3","target":"record","created_at":"2026-05-18T03:56:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"20c301c509fd3e0f6cbd30e8912bbb26eb4e07392a72e4d7b662dbbb59811c49","cross_cats_sorted":["cs.SY","math.OC","q-fin.RM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-06-16T17:00:11Z","title_canon_sha256":"acc8a677c330d9c348daca2ad9834cf824ebd4c27ffaf452458bbbf383502923"},"schema_version":"1.0","source":{"id":"1106.3273","kind":"arxiv","version":2}},"canonical_sha256":"9b1a67e8cab2f051ba15f78d7a136567bbe7ed64813643ab21dc8f0b6e8fa034","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b1a67e8cab2f051ba15f78d7a136567bbe7ed64813643ab21dc8f0b6e8fa034","first_computed_at":"2026-05-18T03:56:22.653652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:22.653652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R0chgfJTvKl4eGjbihEQDmcmlxYDYrGGmUim+iO76OotM6OsDyyEZykP76ZE8+dOOEqkznCFI/iGjJGfgBQaAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:22.654178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.3273","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5e9bf6fb9ad6dcff8ffeab04902110b7c78d8a00510ee8d57110dd70fb214a3","sha256:28fb737669f5624f18521c609080489e9ebbcd888902f7f77e4fc77540cd5a81"],"state_sha256":"3ad380518b7a7494afb74c568544f58c68631bfd3a3d78aeb4e681e7d9020f34"}