{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IDJ7JACPDW5TRQTB5JAY3F4QVA","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":"c25d8e874da0a9f9396f1e274faa81299f92fc8b3f93d138dbd3a324ad8d7142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-08T16:34:44Z","title_canon_sha256":"be628bb9a521208b675da04480899bb8e55bf89da792cf1dec75cbb75f941b1b"},"schema_version":"1.0","source":{"id":"1211.1894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1894","created_at":"2026-05-18T03:41:13Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1894v1","created_at":"2026-05-18T03:41:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1894","created_at":"2026-05-18T03:41:13Z"},{"alias_kind":"pith_short_12","alias_value":"IDJ7JACPDW5T","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IDJ7JACPDW5TRQTB","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IDJ7JACP","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ce7a92699afffd2573b9a292212074c39c6e68e16898185d3296368090927b0c","target":"graph","created_at":"2026-05-18T03:41:13Z","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":"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","authors_text":"A. Genadot, M. Thieullen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-08T16:34:44Z","title":"Multiscale Piecewise Deterministic Markov Process in Infinite Dimension: Central Limit Theorem and Langevin Approximation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1894","kind":"arxiv","version":1},"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":"sha256:0e8a4d61942bc0cee2d9a460bda6b60b8d3530544ba923488ee912dda579900a","target":"record","created_at":"2026-05-18T03:41:13Z","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":"c25d8e874da0a9f9396f1e274faa81299f92fc8b3f93d138dbd3a324ad8d7142","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-08T16:34:44Z","title_canon_sha256":"be628bb9a521208b675da04480899bb8e55bf89da792cf1dec75cbb75f941b1b"},"schema_version":"1.0","source":{"id":"1211.1894","kind":"arxiv","version":1}},"canonical_sha256":"40d3f4804f1dbb38c261ea418d9790a83274eedcc02d0e8cdac9d6f5dd567e4e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40d3f4804f1dbb38c261ea418d9790a83274eedcc02d0e8cdac9d6f5dd567e4e","first_computed_at":"2026-05-18T03:41:13.289065Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:13.289065Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2gPML0J0IWZfHU1lozVX/zAE+on7eT2daG/geSKSqWNWVsFq3TB2JL5tO8a0wQTaCg/6XtRMobh5YucuUMcYBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:13.289569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e8a4d61942bc0cee2d9a460bda6b60b8d3530544ba923488ee912dda579900a","sha256:ce7a92699afffd2573b9a292212074c39c6e68e16898185d3296368090927b0c"],"state_sha256":"b56bdac954af56465b6e36275b822417aef116ec812771ac901236309544b157"}