{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2N5P5BXYEXQOMJ665GQDOZJ23E","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":"d561f657df0425d508414ccef07abefb51316c95b7d12d1ac73d76f87abce988","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-10T14:24:02Z","title_canon_sha256":"f1aee159c00c77f4cd55920a6eaa8bb04f6e4b49e918a5fd3dda9ba8597759dc"},"schema_version":"1.0","source":{"id":"1908.03762","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.03762","created_at":"2026-07-05T01:05:23Z"},{"alias_kind":"arxiv_version","alias_value":"1908.03762v3","created_at":"2026-07-05T01:05:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.03762","created_at":"2026-07-05T01:05:23Z"},{"alias_kind":"pith_short_12","alias_value":"2N5P5BXYEXQO","created_at":"2026-07-05T01:05:23Z"},{"alias_kind":"pith_short_16","alias_value":"2N5P5BXYEXQOMJ66","created_at":"2026-07-05T01:05:23Z"},{"alias_kind":"pith_short_8","alias_value":"2N5P5BXY","created_at":"2026-07-05T01:05:23Z"}],"graph_snapshots":[{"event_id":"sha256:8255a4a12d7799f51ac807c9c43d1b69727133e738f60f1ec0d7e2f246ae7eaa","target":"graph","created_at":"2026-07-05T01:05:23Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1908.03762/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The density-dependent Markov chain (DDMC) introduced in \\cite{Kurtz1978} is a continuous time Markov process applied in fields such as epidemics, chemical reactions and so on. In this paper, we give moderate deviation principles of paths of DDMC under some generally satisfied assumptions. The proofs for the lower and upper bounds of our main result utilize an exponential martingale and a generalized version of Girsanov's theorem. The exponential martingale is defined according to the generator of DDMC.","authors_text":"Xiaofeng Xue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-10T14:24:02Z","title":"Moderate deviations of density-dependent Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.03762","kind":"arxiv","version":3},"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":"sha256:19d18a2f465e6de7f996cfc7ebd2045df0eda3e4b585407fe84a02a2e3df9167","target":"record","created_at":"2026-07-05T01:05:23Z","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":"d561f657df0425d508414ccef07abefb51316c95b7d12d1ac73d76f87abce988","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-08-10T14:24:02Z","title_canon_sha256":"f1aee159c00c77f4cd55920a6eaa8bb04f6e4b49e918a5fd3dda9ba8597759dc"},"schema_version":"1.0","source":{"id":"1908.03762","kind":"arxiv","version":3}},"canonical_sha256":"d37afe86f825e0e627dee9a037653ad923731a32c30f8fa40791f3edafe7a260","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d37afe86f825e0e627dee9a037653ad923731a32c30f8fa40791f3edafe7a260","first_computed_at":"2026-07-05T01:05:23.811110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:05:23.811110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TFfNbUjIO8Ho0iJdoLCexoA80zbWnb97C1+vac0LUkEqREFQdxpJ+GTrW6C6evsLJYdK6JHx/VbgC7YuXELLDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:05:23.811577Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.03762","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19d18a2f465e6de7f996cfc7ebd2045df0eda3e4b585407fe84a02a2e3df9167","sha256:8255a4a12d7799f51ac807c9c43d1b69727133e738f60f1ec0d7e2f246ae7eaa"],"state_sha256":"d64edc7289c271c01d2e1d4abe9b59ed631079ab63a53165af28641fc7484bc4"}