{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:UV5VXKSDJ3IK5A5P7C5OXZOXJT","short_pith_number":"pith:UV5VXKSD","schema_version":"1.0","canonical_sha256":"a57b5baa434ed0ae83aff8baebe5d74cc0702d77a690f96ae0a8cb476b11bd98","source":{"kind":"arxiv","id":"1606.06658","version":3},"attestation_state":"computed","paper":{"title":"On the Quasi-Stationary Distribution of the Shiryaev-Roberts Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Aleksey S. Polunchenko","submitted_at":"2016-06-21T17:00:13Z","abstract_excerpt":"We consider the diffusion $(R_t^r)_{t\\ge0}$ generated by the equation $dR_t^r=dt+\\mu R_t^r dB_t$ with $R_0^r\\triangleq r\\ge0$ fixed, and where $\\mu\\neq0$ is given, and $(B_t)_{t\\ge0}$ is standard Brownian motion. We assume that $(R_t^r)_{t\\ge0}$ is stopped at $\\mathcal{S}_A^r\\triangleq\\inf\\{t\\ge0\\colon R_t^r=A\\}$ with $A>0$ preset, and obtain a closed-from formula for the quasi-stationary distribution of $(R_t^r)_{t\\ge0}$, i.e., the limit $Q_A(x)\\triangleq\\lim_{t\\to+\\infty}\\Pr(R_t^r\\le x|\\mathcal{S}_A^r>t)$, $x\\in[0,A]$. Further, we also prove $Q_A(x)$ to be unimodal for any $A>0$, and obtain "},"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":"1606.06658","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2016-06-21T17:00:13Z","cross_cats_sorted":["math.PR","stat.ME","stat.TH"],"title_canon_sha256":"be72f798486c3fed544ad148f919478b306bb211ff450414664fb747da8f62e9","abstract_canon_sha256":"499f15a0ac47408db33c569e792a1c6bce5c143ef8e93e9f4fc7a493099b4233"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:04.578814Z","signature_b64":"Ma/AHJEQfMG8CYSQItUPPJhXlf0CzyRysNDzCHYnBIZ6v8vfQ+xGlHEbvlq/VMCixJRYtrARRlWuTX2g4EqBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a57b5baa434ed0ae83aff8baebe5d74cc0702d77a690f96ae0a8cb476b11bd98","last_reissued_at":"2026-05-18T00:49:04.578357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:04.578357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Quasi-Stationary Distribution of the Shiryaev-Roberts Diffusion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Aleksey S. Polunchenko","submitted_at":"2016-06-21T17:00:13Z","abstract_excerpt":"We consider the diffusion $(R_t^r)_{t\\ge0}$ generated by the equation $dR_t^r=dt+\\mu R_t^r dB_t$ with $R_0^r\\triangleq r\\ge0$ fixed, and where $\\mu\\neq0$ is given, and $(B_t)_{t\\ge0}$ is standard Brownian motion. We assume that $(R_t^r)_{t\\ge0}$ is stopped at $\\mathcal{S}_A^r\\triangleq\\inf\\{t\\ge0\\colon R_t^r=A\\}$ with $A>0$ preset, and obtain a closed-from formula for the quasi-stationary distribution of $(R_t^r)_{t\\ge0}$, i.e., the limit $Q_A(x)\\triangleq\\lim_{t\\to+\\infty}\\Pr(R_t^r\\le x|\\mathcal{S}_A^r>t)$, $x\\in[0,A]$. Further, we also prove $Q_A(x)$ to be unimodal for any $A>0$, and obtain "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06658","kind":"arxiv","version":3},"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":"1606.06658","created_at":"2026-05-18T00:49:04.578422+00:00"},{"alias_kind":"arxiv_version","alias_value":"1606.06658v3","created_at":"2026-05-18T00:49:04.578422+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06658","created_at":"2026-05-18T00:49:04.578422+00:00"},{"alias_kind":"pith_short_12","alias_value":"UV5VXKSDJ3IK","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_16","alias_value":"UV5VXKSDJ3IK5A5P","created_at":"2026-05-18T12:30:46.583412+00:00"},{"alias_kind":"pith_short_8","alias_value":"UV5VXKSD","created_at":"2026-05-18T12:30:46.583412+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/UV5VXKSDJ3IK5A5P7C5OXZOXJT","json":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT.json","graph_json":"https://pith.science/api/pith-number/UV5VXKSDJ3IK5A5P7C5OXZOXJT/graph.json","events_json":"https://pith.science/api/pith-number/UV5VXKSDJ3IK5A5P7C5OXZOXJT/events.json","paper":"https://pith.science/paper/UV5VXKSD"},"agent_actions":{"view_html":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT","download_json":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT.json","view_paper":"https://pith.science/paper/UV5VXKSD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1606.06658&json=true","fetch_graph":"https://pith.science/api/pith-number/UV5VXKSDJ3IK5A5P7C5OXZOXJT/graph.json","fetch_events":"https://pith.science/api/pith-number/UV5VXKSDJ3IK5A5P7C5OXZOXJT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT/action/storage_attestation","attest_author":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT/action/author_attestation","sign_citation":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT/action/citation_signature","submit_replication":"https://pith.science/pith/UV5VXKSDJ3IK5A5P7C5OXZOXJT/action/replication_record"}},"created_at":"2026-05-18T00:49:04.578422+00:00","updated_at":"2026-05-18T00:49:04.578422+00:00"}