{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ANIG2LRBLQ7L2NBL42T6D52WHY","short_pith_number":"pith:ANIG2LRB","schema_version":"1.0","canonical_sha256":"03506d2e215c3ebd342be6a7e1f7563e2df49e55c82d24099ba0ae17d4b87645","source":{"kind":"arxiv","id":"1306.5353","version":1},"attestation_state":"computed","paper":{"title":"A local limit theorem for densities of the additive component of a finite Markov Additive Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"James Ledoux (IRMAR), Lo\\\"ic Herv\\'e (IRMAR)","submitted_at":"2013-06-22T21:12:27Z","abstract_excerpt":"In this paper, we are concerned with centered Markov Additive Processes $\\{(X_t,Y_t)\\}_{t\\in\\T}$ where the driving Markov process $\\{X_t\\}_{t\\in\\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for the density of the absolutely continuous part of the probability distribution of $t^{-1/2}Y_t$ given $X_0$. The rate of convergence and the moment condition are the expected ones with respect to the i.i.d case. An application to the joint distribution of local times of a finite jump process is sketched."},"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":"1306.5353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-22T21:12:27Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"5204fe02f7c54a731e6c60c164b4a006fe37fc88f8845e5013f115c028487dc4","abstract_canon_sha256":"6179f1448e710edabfc1089750ce9477a395188df287f5c9070b8d7480e89d02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:08.416153Z","signature_b64":"iSk+upw5Ff6pd2TfD7fEwWnp1hykCPiM99DvroYZTI8Q9b7PaUqlSBbWXmQz9KbttCe15mxE+0k2a/E6YY3yDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03506d2e215c3ebd342be6a7e1f7563e2df49e55c82d24099ba0ae17d4b87645","last_reissued_at":"2026-05-18T03:20:08.415539Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:08.415539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A local limit theorem for densities of the additive component of a finite Markov Additive Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"James Ledoux (IRMAR), Lo\\\"ic Herv\\'e (IRMAR)","submitted_at":"2013-06-22T21:12:27Z","abstract_excerpt":"In this paper, we are concerned with centered Markov Additive Processes $\\{(X_t,Y_t)\\}_{t\\in\\T}$ where the driving Markov process $\\{X_t\\}_{t\\in\\T}$ has a finite state space. Under suitable conditions, we provide a local limit theorem for the density of the absolutely continuous part of the probability distribution of $t^{-1/2}Y_t$ given $X_0$. The rate of convergence and the moment condition are the expected ones with respect to the i.i.d case. An application to the joint distribution of local times of a finite jump process is sketched."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5353","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":"1306.5353","created_at":"2026-05-18T03:20:08.415634+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.5353v1","created_at":"2026-05-18T03:20:08.415634+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.5353","created_at":"2026-05-18T03:20:08.415634+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANIG2LRBLQ7L","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANIG2LRBLQ7L2NBL","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANIG2LRB","created_at":"2026-05-18T12:27:38.830355+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/ANIG2LRBLQ7L2NBL42T6D52WHY","json":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY.json","graph_json":"https://pith.science/api/pith-number/ANIG2LRBLQ7L2NBL42T6D52WHY/graph.json","events_json":"https://pith.science/api/pith-number/ANIG2LRBLQ7L2NBL42T6D52WHY/events.json","paper":"https://pith.science/paper/ANIG2LRB"},"agent_actions":{"view_html":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY","download_json":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY.json","view_paper":"https://pith.science/paper/ANIG2LRB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.5353&json=true","fetch_graph":"https://pith.science/api/pith-number/ANIG2LRBLQ7L2NBL42T6D52WHY/graph.json","fetch_events":"https://pith.science/api/pith-number/ANIG2LRBLQ7L2NBL42T6D52WHY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY/action/storage_attestation","attest_author":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY/action/author_attestation","sign_citation":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY/action/citation_signature","submit_replication":"https://pith.science/pith/ANIG2LRBLQ7L2NBL42T6D52WHY/action/replication_record"}},"created_at":"2026-05-18T03:20:08.415634+00:00","updated_at":"2026-05-18T03:20:08.415634+00:00"}