{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:C4TC54JPYF45F6LZNX3QYS4K63","short_pith_number":"pith:C4TC54JP","schema_version":"1.0","canonical_sha256":"17262ef12fc179d2f9796df70c4b8af6d34c28e3b66a44f34e47ce89b2456420","source":{"kind":"arxiv","id":"1707.06129","version":1},"attestation_state":"computed","paper":{"title":"Conditioned local limit theorems for random walks defined on finite Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emile Le Page, Ion Grama, Ronan Lauvergnat","submitted_at":"2017-07-19T14:48:42Z","abstract_excerpt":"Let $(X_n)_{n\\geq 0}$ be a Markov chain with values in a finite state space $\\mathbb X$ starting at $X_0=x \\in \\mathbb X$ and let $f$ be a real function defined on $\\mathbb X$. Set $S_n=\\sum_{k=1}^{n} f(X_k)$, $n\\geqslant 1$. For any $y \\in \\mathbb R$ denote by $\\tau_y$ the first time when $y+S_n$ becomes non-positive. We study the asymptotic behaviour of the probability $\\mathbb P_x \\left( y+S_{n} \\in [z,z+a] \\,,\\, \\tau_y > n \\right)$ as $n\\to+\\infty.$ We first establish for this probability a conditional version of the local limit theorem of Stone. Then we find for it an asymptotic equivalen"},"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":"1707.06129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-19T14:48:42Z","cross_cats_sorted":[],"title_canon_sha256":"015c24dc16c25838a7e83313301fd8e9602a02d0773bc627cf42355350361691","abstract_canon_sha256":"6c05de0dd331d9663ef8ffacfeac2062ae5c183e251ecbd2db967e3eea3725e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:57.569657Z","signature_b64":"P/Sn54K17sWweBxLbRZkHEmx9veWgPBYunc0znfDlz7xSR6B+npGhVRvcyDzmPUhXIYoukmJs5jctIgDl/SnDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17262ef12fc179d2f9796df70c4b8af6d34c28e3b66a44f34e47ce89b2456420","last_reissued_at":"2026-05-18T00:39:57.569145Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:57.569145Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Conditioned local limit theorems for random walks defined on finite Markov chains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emile Le Page, Ion Grama, Ronan Lauvergnat","submitted_at":"2017-07-19T14:48:42Z","abstract_excerpt":"Let $(X_n)_{n\\geq 0}$ be a Markov chain with values in a finite state space $\\mathbb X$ starting at $X_0=x \\in \\mathbb X$ and let $f$ be a real function defined on $\\mathbb X$. Set $S_n=\\sum_{k=1}^{n} f(X_k)$, $n\\geqslant 1$. For any $y \\in \\mathbb R$ denote by $\\tau_y$ the first time when $y+S_n$ becomes non-positive. We study the asymptotic behaviour of the probability $\\mathbb P_x \\left( y+S_{n} \\in [z,z+a] \\,,\\, \\tau_y > n \\right)$ as $n\\to+\\infty.$ We first establish for this probability a conditional version of the local limit theorem of Stone. Then we find for it an asymptotic equivalen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.06129","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":"1707.06129","created_at":"2026-05-18T00:39:57.569214+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.06129v1","created_at":"2026-05-18T00:39:57.569214+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.06129","created_at":"2026-05-18T00:39:57.569214+00:00"},{"alias_kind":"pith_short_12","alias_value":"C4TC54JPYF45","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"C4TC54JPYF45F6LZ","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"C4TC54JP","created_at":"2026-05-18T12:31:08.081275+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.02456","citing_title":"Precise large deviation asymptotics for products of random matrices","ref_index":18,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63","json":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63.json","graph_json":"https://pith.science/api/pith-number/C4TC54JPYF45F6LZNX3QYS4K63/graph.json","events_json":"https://pith.science/api/pith-number/C4TC54JPYF45F6LZNX3QYS4K63/events.json","paper":"https://pith.science/paper/C4TC54JP"},"agent_actions":{"view_html":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63","download_json":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63.json","view_paper":"https://pith.science/paper/C4TC54JP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.06129&json=true","fetch_graph":"https://pith.science/api/pith-number/C4TC54JPYF45F6LZNX3QYS4K63/graph.json","fetch_events":"https://pith.science/api/pith-number/C4TC54JPYF45F6LZNX3QYS4K63/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63/action/storage_attestation","attest_author":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63/action/author_attestation","sign_citation":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63/action/citation_signature","submit_replication":"https://pith.science/pith/C4TC54JPYF45F6LZNX3QYS4K63/action/replication_record"}},"created_at":"2026-05-18T00:39:57.569214+00:00","updated_at":"2026-05-18T00:39:57.569214+00:00"}