{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:26NGI54SMTTH7LRKQSTS7SWPKR","short_pith_number":"pith:26NGI54S","schema_version":"1.0","canonical_sha256":"d79a64779264e67fae2a84a72fcacf546cdb697b2182c4098e90080c48ab6c14","source":{"kind":"arxiv","id":"1105.0270","version":2},"attestation_state":"computed","paper":{"title":"Stability of a Markov-modulated Markov Chain, with application to a wireless network governed by two protocols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrey Tyurlikov, Sergey Foss, Seva Shneer","submitted_at":"2011-05-02T09:17:33Z","abstract_excerpt":"We consider a discrete-time Markov chain $(X^t,Y^t)$, $t=0,1,2,...$, where the $X$-component forms a Markov chain itself. Assume that $(X^t)$ is Harris-ergodic and consider an auxiliary Markov chain ${\\hat{Y}^t}$ whose transition probabilities are the averages of transition probabilities of the $Y$-component of the $(X,Y)$-chain, where the averaging is weighted by the stationary distribution of the $X$-component.\n  We first provide natural conditions in terms of test functions ensuring that the $\\hat{Y}$-chain is positive recurrent and then prove that these conditions are also sufficient for p"},"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":"1105.0270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-05-02T09:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"596aadcf4b7ea486d223225c3dd2419962349a51f0205f83509982d7405bb14e","abstract_canon_sha256":"0a47cef57447b161e893e4ee4cde78f6a825025be2fa8c118a169cd0fa830ada"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:00.091913Z","signature_b64":"YjKLxJ+jY7Qvjg+neiKgL+rWlL0FfrrBwMIlTuq9A/cJVLWsXysywMQ7UD8BhqRTXbR0rJbE5mstUyQ8DC/bDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d79a64779264e67fae2a84a72fcacf546cdb697b2182c4098e90080c48ab6c14","last_reissued_at":"2026-05-18T03:34:00.091108Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:00.091108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of a Markov-modulated Markov Chain, with application to a wireless network governed by two protocols","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Andrey Tyurlikov, Sergey Foss, Seva Shneer","submitted_at":"2011-05-02T09:17:33Z","abstract_excerpt":"We consider a discrete-time Markov chain $(X^t,Y^t)$, $t=0,1,2,...$, where the $X$-component forms a Markov chain itself. Assume that $(X^t)$ is Harris-ergodic and consider an auxiliary Markov chain ${\\hat{Y}^t}$ whose transition probabilities are the averages of transition probabilities of the $Y$-component of the $(X,Y)$-chain, where the averaging is weighted by the stationary distribution of the $X$-component.\n  We first provide natural conditions in terms of test functions ensuring that the $\\hat{Y}$-chain is positive recurrent and then prove that these conditions are also sufficient for p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.0270","kind":"arxiv","version":2},"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":"1105.0270","created_at":"2026-05-18T03:34:00.091244+00:00"},{"alias_kind":"arxiv_version","alias_value":"1105.0270v2","created_at":"2026-05-18T03:34:00.091244+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.0270","created_at":"2026-05-18T03:34:00.091244+00:00"},{"alias_kind":"pith_short_12","alias_value":"26NGI54SMTTH","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"26NGI54SMTTH7LRK","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"26NGI54S","created_at":"2026-05-18T12:26:18.847500+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/26NGI54SMTTH7LRKQSTS7SWPKR","json":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR.json","graph_json":"https://pith.science/api/pith-number/26NGI54SMTTH7LRKQSTS7SWPKR/graph.json","events_json":"https://pith.science/api/pith-number/26NGI54SMTTH7LRKQSTS7SWPKR/events.json","paper":"https://pith.science/paper/26NGI54S"},"agent_actions":{"view_html":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR","download_json":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR.json","view_paper":"https://pith.science/paper/26NGI54S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1105.0270&json=true","fetch_graph":"https://pith.science/api/pith-number/26NGI54SMTTH7LRKQSTS7SWPKR/graph.json","fetch_events":"https://pith.science/api/pith-number/26NGI54SMTTH7LRKQSTS7SWPKR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR/action/storage_attestation","attest_author":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR/action/author_attestation","sign_citation":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR/action/citation_signature","submit_replication":"https://pith.science/pith/26NGI54SMTTH7LRKQSTS7SWPKR/action/replication_record"}},"created_at":"2026-05-18T03:34:00.091244+00:00","updated_at":"2026-05-18T03:34:00.091244+00:00"}