{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:F533YDZGDV575IG5Y5UAJ3KH6T","short_pith_number":"pith:F533YDZG","schema_version":"1.0","canonical_sha256":"2f77bc0f261d7bfea0ddc76804ed47f4c675460b46cd6115922fa6b3a0ad62c0","source":{"kind":"arxiv","id":"1401.0364","version":1},"attestation_state":"computed","paper":{"title":"Theoretical analysis of a Stochastic Approximation approach for computing Quasi-Stationary distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jose Blanchet, Peter Glynn, Shuheng Zheng","submitted_at":"2014-01-02T04:10:20Z","abstract_excerpt":"This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for explicit transition matrix manipulation to extract the principal eigenvector. Our paper analyzes the algorithm by casting it as a stochastic approximation algorithm (Robbins-Monro) [23, 16]. In doing so, we prove its convergence and obtain its rate of convergence. Based on this insight, we also give an example where the rate of convergence is very slow. This 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":"1401.0364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-01-02T04:10:20Z","cross_cats_sorted":[],"title_canon_sha256":"0c4aab510ea92fb64f72e41020b9899d3f5f49e89cdde292a17d061fa9df3568","abstract_canon_sha256":"b322404a9ded595aecabbbf3b14e9a99891e7288d9c0149f73502c7978e42a57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:03:23.424046Z","signature_b64":"0e3sPDoGDtsQEh+sYnU+JWyUhUbC7Np9eJkbX+ibmKwecZ7HDF+9EGQQAZ9Cp3M/XSA4fRFCwlAV0KI0hAQ0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f77bc0f261d7bfea0ddc76804ed47f4c675460b46cd6115922fa6b3a0ad62c0","last_reissued_at":"2026-05-18T03:03:23.423211Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:03:23.423211Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Theoretical analysis of a Stochastic Approximation approach for computing Quasi-Stationary distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jose Blanchet, Peter Glynn, Shuheng Zheng","submitted_at":"2014-01-02T04:10:20Z","abstract_excerpt":"This paper studies a method, which has been proposed in the Physics literature by [8, 7, 10], for estimating the quasi-stationary distribution. In contrast to existing methods in eigenvector estimation, the method eliminates the need for explicit transition matrix manipulation to extract the principal eigenvector. Our paper analyzes the algorithm by casting it as a stochastic approximation algorithm (Robbins-Monro) [23, 16]. In doing so, we prove its convergence and obtain its rate of convergence. Based on this insight, we also give an example where the rate of convergence is very slow. This p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0364","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":"1401.0364","created_at":"2026-05-18T03:03:23.423365+00:00"},{"alias_kind":"arxiv_version","alias_value":"1401.0364v1","created_at":"2026-05-18T03:03:23.423365+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0364","created_at":"2026-05-18T03:03:23.423365+00:00"},{"alias_kind":"pith_short_12","alias_value":"F533YDZGDV57","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_16","alias_value":"F533YDZGDV575IG5","created_at":"2026-05-18T12:28:28.263976+00:00"},{"alias_kind":"pith_short_8","alias_value":"F533YDZG","created_at":"2026-05-18T12:28:28.263976+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/F533YDZGDV575IG5Y5UAJ3KH6T","json":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T.json","graph_json":"https://pith.science/api/pith-number/F533YDZGDV575IG5Y5UAJ3KH6T/graph.json","events_json":"https://pith.science/api/pith-number/F533YDZGDV575IG5Y5UAJ3KH6T/events.json","paper":"https://pith.science/paper/F533YDZG"},"agent_actions":{"view_html":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T","download_json":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T.json","view_paper":"https://pith.science/paper/F533YDZG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1401.0364&json=true","fetch_graph":"https://pith.science/api/pith-number/F533YDZGDV575IG5Y5UAJ3KH6T/graph.json","fetch_events":"https://pith.science/api/pith-number/F533YDZGDV575IG5Y5UAJ3KH6T/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T/action/storage_attestation","attest_author":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T/action/author_attestation","sign_citation":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T/action/citation_signature","submit_replication":"https://pith.science/pith/F533YDZGDV575IG5Y5UAJ3KH6T/action/replication_record"}},"created_at":"2026-05-18T03:03:23.423365+00:00","updated_at":"2026-05-18T03:03:23.423365+00:00"}