{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:JPEKTRLPEOYLTPJRDP7LEKXVLT","short_pith_number":"pith:JPEKTRLP","schema_version":"1.0","canonical_sha256":"4bc8a9c56f23b0b9bd311bfeb22af55cc1664a9aed6d2e7a2cbe86701002860c","source":{"kind":"arxiv","id":"1509.01704","version":1},"attestation_state":"computed","paper":{"title":"Renewal approximation for the absorption time of a decreasing Markov chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Gerold Alsmeyer","submitted_at":"2015-09-05T14:48:19Z","abstract_excerpt":"We consider a Markov chain $(M_{n})_{n\\ge 0}$ on the set $\\mathbb{N}_{0}$ of nonnegative integers which is eventually decreasing, i.e. $\\mathbb{P}\\{M_{n+1}<M_{n}|M_{n}\\ge a\\}=1$ for some $a\\in\\mathbb{N}$ and all $n\\ge 0$. We are interested in the asymptotic behaviour of the law of the stopping time $T=T(a):=\\inf\\{k\\in\\mathbb{N}_{0}: M_{k}<a\\}$ under $\\mathbb{P}_{n}:=\\mathbb{P}(\\cdot|M_{0}=n)$ as $n\\to\\infty$. Assuming that the decrements of $(M_{n})_{n\\ge 0}$ given $M_{0}=n$ possess a kind of stationarity for large $n$, we derive sufficient conditions for the convergence in minimal $L^{p}$-dis"},"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":"1509.01704","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-05T14:48:19Z","cross_cats_sorted":[],"title_canon_sha256":"ac5baa74ad4ec0f5911e7768fc5c8e2016219f4d4d2dfab0af88456df5df7e07","abstract_canon_sha256":"5034350288e75b8f34f955ecbb7f8e02ba15cc5304d65709da8864d7e27dc783"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:50.800489Z","signature_b64":"xNHFKgauqJ6tF2ZaujW/fUQUwuyAxUD0uGFqJ//g8s0W9TQExutmE4lBKWOl/3TKFQGDGbwTl6tKcLjWUw9dCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc8a9c56f23b0b9bd311bfeb22af55cc1664a9aed6d2e7a2cbe86701002860c","last_reissued_at":"2026-05-18T01:33:50.800014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:50.800014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renewal approximation for the absorption time of a decreasing Markov chain","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Gerold Alsmeyer","submitted_at":"2015-09-05T14:48:19Z","abstract_excerpt":"We consider a Markov chain $(M_{n})_{n\\ge 0}$ on the set $\\mathbb{N}_{0}$ of nonnegative integers which is eventually decreasing, i.e. $\\mathbb{P}\\{M_{n+1}<M_{n}|M_{n}\\ge a\\}=1$ for some $a\\in\\mathbb{N}$ and all $n\\ge 0$. We are interested in the asymptotic behaviour of the law of the stopping time $T=T(a):=\\inf\\{k\\in\\mathbb{N}_{0}: M_{k}<a\\}$ under $\\mathbb{P}_{n}:=\\mathbb{P}(\\cdot|M_{0}=n)$ as $n\\to\\infty$. Assuming that the decrements of $(M_{n})_{n\\ge 0}$ given $M_{0}=n$ possess a kind of stationarity for large $n$, we derive sufficient conditions for the convergence in minimal $L^{p}$-dis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01704","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":"1509.01704","created_at":"2026-05-18T01:33:50.800084+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.01704v1","created_at":"2026-05-18T01:33:50.800084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01704","created_at":"2026-05-18T01:33:50.800084+00:00"},{"alias_kind":"pith_short_12","alias_value":"JPEKTRLPEOYL","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_16","alias_value":"JPEKTRLPEOYLTPJR","created_at":"2026-05-18T12:29:27.538025+00:00"},{"alias_kind":"pith_short_8","alias_value":"JPEKTRLP","created_at":"2026-05-18T12:29:27.538025+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/JPEKTRLPEOYLTPJRDP7LEKXVLT","json":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT.json","graph_json":"https://pith.science/api/pith-number/JPEKTRLPEOYLTPJRDP7LEKXVLT/graph.json","events_json":"https://pith.science/api/pith-number/JPEKTRLPEOYLTPJRDP7LEKXVLT/events.json","paper":"https://pith.science/paper/JPEKTRLP"},"agent_actions":{"view_html":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT","download_json":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT.json","view_paper":"https://pith.science/paper/JPEKTRLP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.01704&json=true","fetch_graph":"https://pith.science/api/pith-number/JPEKTRLPEOYLTPJRDP7LEKXVLT/graph.json","fetch_events":"https://pith.science/api/pith-number/JPEKTRLPEOYLTPJRDP7LEKXVLT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT/action/storage_attestation","attest_author":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT/action/author_attestation","sign_citation":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT/action/citation_signature","submit_replication":"https://pith.science/pith/JPEKTRLPEOYLTPJRDP7LEKXVLT/action/replication_record"}},"created_at":"2026-05-18T01:33:50.800084+00:00","updated_at":"2026-05-18T01:33:50.800084+00:00"}