{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:IDJ7JACPDW5TRQTB5JAY3F4QVA","short_pith_number":"pith:IDJ7JACP","schema_version":"1.0","canonical_sha256":"40d3f4804f1dbb38c261ea418d9790a83274eedcc02d0e8cdac9d6f5dd567e4e","source":{"kind":"arxiv","id":"1211.1894","version":1},"attestation_state":"computed","paper":{"title":"Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Genadot, M. Thieullen","submitted_at":"2012-11-08T16:34:44Z","abstract_excerpt":"In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuation of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated Langevin approximation is considered. The motivation of this work is a stochastic Hodgkin-Huxley model which describes the propagation of an action potential along the nerve fiber. We study this PDMP in detail and provide more general results fo"},"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":"1211.1894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-08T16:34:44Z","cross_cats_sorted":[],"title_canon_sha256":"be628bb9a521208b675da04480899bb8e55bf89da792cf1dec75cbb75f941b1b","abstract_canon_sha256":"c25d8e874da0a9f9396f1e274faa81299f92fc8b3f93d138dbd3a324ad8d7142"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:13.289569Z","signature_b64":"2gPML0J0IWZfHU1lozVX/zAE+on7eT2daG/geSKSqWNWVsFq3TB2JL5tO8a0wQTaCg/6XtRMobh5YucuUMcYBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40d3f4804f1dbb38c261ea418d9790a83274eedcc02d0e8cdac9d6f5dd567e4e","last_reissued_at":"2026-05-18T03:41:13.289065Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:13.289065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Genadot, M. Thieullen","submitted_at":"2012-11-08T16:34:44Z","abstract_excerpt":"In [20], the authors addressed the question of the averaging of a slow-fast Piecewise Deterministic Markov Process (PDMP) in infinite dimension. In the present paper, we carry on and complete this work by the mathematical analysis of the fluctuation of the slow-fast system around the averaged limit. A central limit theorem is derived and the associated Langevin approximation is considered. The motivation of this work is a stochastic Hodgkin-Huxley model which describes the propagation of an action potential along the nerve fiber. We study this PDMP in detail and provide more general results fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1894","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":"1211.1894","created_at":"2026-05-18T03:41:13.289139+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.1894v1","created_at":"2026-05-18T03:41:13.289139+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1894","created_at":"2026-05-18T03:41:13.289139+00:00"},{"alias_kind":"pith_short_12","alias_value":"IDJ7JACPDW5T","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"IDJ7JACPDW5TRQTB","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"IDJ7JACP","created_at":"2026-05-18T12:27:09.501522+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/IDJ7JACPDW5TRQTB5JAY3F4QVA","json":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA.json","graph_json":"https://pith.science/api/pith-number/IDJ7JACPDW5TRQTB5JAY3F4QVA/graph.json","events_json":"https://pith.science/api/pith-number/IDJ7JACPDW5TRQTB5JAY3F4QVA/events.json","paper":"https://pith.science/paper/IDJ7JACP"},"agent_actions":{"view_html":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA","download_json":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA.json","view_paper":"https://pith.science/paper/IDJ7JACP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.1894&json=true","fetch_graph":"https://pith.science/api/pith-number/IDJ7JACPDW5TRQTB5JAY3F4QVA/graph.json","fetch_events":"https://pith.science/api/pith-number/IDJ7JACPDW5TRQTB5JAY3F4QVA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA/action/storage_attestation","attest_author":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA/action/author_attestation","sign_citation":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA/action/citation_signature","submit_replication":"https://pith.science/pith/IDJ7JACPDW5TRQTB5JAY3F4QVA/action/replication_record"}},"created_at":"2026-05-18T03:41:13.289139+00:00","updated_at":"2026-05-18T03:41:13.289139+00:00"}