{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:VH6PMQXLRTX5FABK54DMUEI7U2","short_pith_number":"pith:VH6PMQXL","schema_version":"1.0","canonical_sha256":"a9fcf642eb8cefd2802aef06ca111fa6b3913ad8b7504be65940df5ddcb745c4","source":{"kind":"arxiv","id":"1407.1215","version":1},"attestation_state":"computed","paper":{"title":"Mean-field stochastic differential equations and associated PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Catherine Rainer, Juan Li, Rainer Buckdahn, Shige Peng","submitted_at":"2014-07-04T13:06:25Z","abstract_excerpt":"In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data $(t,x)\\in[0,T]\\times R^d,$ which coefficients depend on both the solution $X^{t,x}_s$ but also its law. By considering square integrable random variables $\\xi$ as initial condition for this equation, we can easily show the flow property of the solution $X^{t,\\xi}_s$ of this new equation. Associating it with a process $X^{t,x,P_\\xi}_s$ which coincides with $X^{t,\\xi}_s$, when one substitutes $\\xi$ for $x$, but which has the advantage to depend only on the law $P_\\xi$ 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":"1407.1215","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-04T13:06:25Z","cross_cats_sorted":[],"title_canon_sha256":"2cc93f339332b69bfea5f0794abf63287e5cc443fa444167e5972d0cbc135a60","abstract_canon_sha256":"252d5a35fb95895b738b548709ddb611117ea1ad016044ce48331a1c72cc4a5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:18.373061Z","signature_b64":"j0yJrEOMDObd9KyZMQkCRUHgmsyT90pPctixSn2XHAZRQFcqY+DmGvOJyAZd8ZRGl7WRn/eIulN7nGKiAmLvDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a9fcf642eb8cefd2802aef06ca111fa6b3913ad8b7504be65940df5ddcb745c4","last_reissued_at":"2026-05-18T02:48:18.372433Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:18.372433Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Mean-field stochastic differential equations and associated PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Catherine Rainer, Juan Li, Rainer Buckdahn, Shige Peng","submitted_at":"2014-07-04T13:06:25Z","abstract_excerpt":"In this paper we consider a mean-field stochastic differential equation, also called Mc Kean-Vlasov equation, with initial data $(t,x)\\in[0,T]\\times R^d,$ which coefficients depend on both the solution $X^{t,x}_s$ but also its law. By considering square integrable random variables $\\xi$ as initial condition for this equation, we can easily show the flow property of the solution $X^{t,\\xi}_s$ of this new equation. Associating it with a process $X^{t,x,P_\\xi}_s$ which coincides with $X^{t,\\xi}_s$, when one substitutes $\\xi$ for $x$, but which has the advantage to depend only on the law $P_\\xi$ o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.1215","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":"1407.1215","created_at":"2026-05-18T02:48:18.372526+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.1215v1","created_at":"2026-05-18T02:48:18.372526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.1215","created_at":"2026-05-18T02:48:18.372526+00:00"},{"alias_kind":"pith_short_12","alias_value":"VH6PMQXLRTX5","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"VH6PMQXLRTX5FABK","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"VH6PMQXL","created_at":"2026-05-18T12:28:54.890064+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/VH6PMQXLRTX5FABK54DMUEI7U2","json":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2.json","graph_json":"https://pith.science/api/pith-number/VH6PMQXLRTX5FABK54DMUEI7U2/graph.json","events_json":"https://pith.science/api/pith-number/VH6PMQXLRTX5FABK54DMUEI7U2/events.json","paper":"https://pith.science/paper/VH6PMQXL"},"agent_actions":{"view_html":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2","download_json":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2.json","view_paper":"https://pith.science/paper/VH6PMQXL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.1215&json=true","fetch_graph":"https://pith.science/api/pith-number/VH6PMQXLRTX5FABK54DMUEI7U2/graph.json","fetch_events":"https://pith.science/api/pith-number/VH6PMQXLRTX5FABK54DMUEI7U2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2/action/storage_attestation","attest_author":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2/action/author_attestation","sign_citation":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2/action/citation_signature","submit_replication":"https://pith.science/pith/VH6PMQXLRTX5FABK54DMUEI7U2/action/replication_record"}},"created_at":"2026-05-18T02:48:18.372526+00:00","updated_at":"2026-05-18T02:48:18.372526+00:00"}