{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:MMLR63WXIJ7X63G6RVZS34ATFF","short_pith_number":"pith:MMLR63WX","schema_version":"1.0","canonical_sha256":"63171f6ed7427f7f6cde8d732df0132953f58455783cab0b7257118925e10a32","source":{"kind":"arxiv","id":"1009.3862","version":3},"attestation_state":"computed","paper":{"title":"Optimal stopping in a general framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Magdalena Kobylanski (LAMA), Marie-Claire Quenez (LPMA)","submitted_at":"2010-09-20T15:46:30Z","abstract_excerpt":"We study the optimal stopping time problem $v(S)={\\rm ess}\\sup_{\\theta \\geq S} E[\\phi(\\theta)|\\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\\phi(\\theta),\\theta\\in\\mathcal{T}_0)$ \\emph{of non negative random variables} indexed by stopping times. We solve the problem under weak assumptions in terms of integrability and regularity of the reward family. More precisely, we only suppose $v(0) < + \\infty$ and $ (\\phi(\\theta),\\theta\\in \\mathcal{T}_0)$ upper semicontinuous along stopping times in expectation. We show the existence of an optimal stopping time and o"},"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":"1009.3862","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-20T15:46:30Z","cross_cats_sorted":[],"title_canon_sha256":"ec5efd02a210c74ea6adeb5c59efbed55b8a6ac67f38c7b6cafc2a801b60e552","abstract_canon_sha256":"4862abebdbd37ad68f87e7a2d23a1fd0f752f316f6c25c75313ad7e6656683b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:17.321634Z","signature_b64":"bQj4GjtY9bc7ioaW+HpFzKtYCPgFOH8qRWCZZplZmDsJqbAkaNw1jQCFf2N3Pu0eQunNTEiDnCY3OdazUnGSCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63171f6ed7427f7f6cde8d732df0132953f58455783cab0b7257118925e10a32","last_reissued_at":"2026-05-18T03:32:17.321047Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:17.321047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal stopping in a general framework","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Magdalena Kobylanski (LAMA), Marie-Claire Quenez (LPMA)","submitted_at":"2010-09-20T15:46:30Z","abstract_excerpt":"We study the optimal stopping time problem $v(S)={\\rm ess}\\sup_{\\theta \\geq S} E[\\phi(\\theta)|\\mathcal {F}_S]$, for any stopping time $S$, where the reward is given by a family $(\\phi(\\theta),\\theta\\in\\mathcal{T}_0)$ \\emph{of non negative random variables} indexed by stopping times. We solve the problem under weak assumptions in terms of integrability and regularity of the reward family. More precisely, we only suppose $v(0) < + \\infty$ and $ (\\phi(\\theta),\\theta\\in \\mathcal{T}_0)$ upper semicontinuous along stopping times in expectation. We show the existence of an optimal stopping time and o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3862","kind":"arxiv","version":3},"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":"1009.3862","created_at":"2026-05-18T03:32:17.321119+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3862v3","created_at":"2026-05-18T03:32:17.321119+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3862","created_at":"2026-05-18T03:32:17.321119+00:00"},{"alias_kind":"pith_short_12","alias_value":"MMLR63WXIJ7X","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_16","alias_value":"MMLR63WXIJ7X63G6","created_at":"2026-05-18T12:26:10.704358+00:00"},{"alias_kind":"pith_short_8","alias_value":"MMLR63WX","created_at":"2026-05-18T12:26:10.704358+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/MMLR63WXIJ7X63G6RVZS34ATFF","json":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF.json","graph_json":"https://pith.science/api/pith-number/MMLR63WXIJ7X63G6RVZS34ATFF/graph.json","events_json":"https://pith.science/api/pith-number/MMLR63WXIJ7X63G6RVZS34ATFF/events.json","paper":"https://pith.science/paper/MMLR63WX"},"agent_actions":{"view_html":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF","download_json":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF.json","view_paper":"https://pith.science/paper/MMLR63WX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3862&json=true","fetch_graph":"https://pith.science/api/pith-number/MMLR63WXIJ7X63G6RVZS34ATFF/graph.json","fetch_events":"https://pith.science/api/pith-number/MMLR63WXIJ7X63G6RVZS34ATFF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF/action/storage_attestation","attest_author":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF/action/author_attestation","sign_citation":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF/action/citation_signature","submit_replication":"https://pith.science/pith/MMLR63WXIJ7X63G6RVZS34ATFF/action/replication_record"}},"created_at":"2026-05-18T03:32:17.321119+00:00","updated_at":"2026-05-18T03:32:17.321119+00:00"}