{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZND7GZPJPJOFOXKVHEFAV7HJ4G","short_pith_number":"pith:ZND7GZPJ","schema_version":"1.0","canonical_sha256":"cb47f365e97a5c575d55390a0afce9e19c77b6436bd9eaf2c4bb52827a503040","source":{"kind":"arxiv","id":"1801.02999","version":4},"attestation_state":"computed","paper":{"title":"Exact asymptotics for a multi-timescale model, with applications in modeling overdispersed customer streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariska Heemskerk, Michel Mandjes","submitted_at":"2018-01-09T15:32:52Z","abstract_excerpt":"In this paper we study the probability $\\xi_n(u):={\\mathbb P}\\left(C_n\\geqslant u n \\right)$, with $C_n:=A(\\psi_n B(\\varphi_n))$ for L\\'{e}vy processes $A(\\cdot)$ and $B(\\cdot)$, and $\\varphi_n$ and $\\psi_n$ non-negative sequences such that $\\varphi_n \\psi_n =n$ and $\\varphi_n\\to\\infty$ as $n\\to\\infty$. Two timescale regimes are distinguished: a `fast' regime in which $\\varphi_n$ is superlinear and a `slow' regime in which $\\varphi_n$ is sublinear. We provide the exact asymptotics of $\\xi_n(u)$ (as $n\\to\\infty$) for both regimes, relying on change-of-measure arguments in combination with Edgew"},"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":"1801.02999","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-01-09T15:32:52Z","cross_cats_sorted":[],"title_canon_sha256":"f488990e3673cc8d6b93f51c28c0f7804d497f353fd21cdf63971e9c2e10cf82","abstract_canon_sha256":"a32c00d99ec00e0a36cebd49c38282786c90a5c7b84694d398a3339302e99c1b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:08.156727Z","signature_b64":"UlpTUyJK7juLbgSerBeeT7X6pOpfqjrQaepiMKwiLdUyxGePGgLmvGAx+T93A4XYzqVKycP2Pl1nzyCtXCJAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb47f365e97a5c575d55390a0afce9e19c77b6436bd9eaf2c4bb52827a503040","last_reissued_at":"2026-05-17T23:52:08.156208Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:08.156208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exact asymptotics for a multi-timescale model, with applications in modeling overdispersed customer streams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariska Heemskerk, Michel Mandjes","submitted_at":"2018-01-09T15:32:52Z","abstract_excerpt":"In this paper we study the probability $\\xi_n(u):={\\mathbb P}\\left(C_n\\geqslant u n \\right)$, with $C_n:=A(\\psi_n B(\\varphi_n))$ for L\\'{e}vy processes $A(\\cdot)$ and $B(\\cdot)$, and $\\varphi_n$ and $\\psi_n$ non-negative sequences such that $\\varphi_n \\psi_n =n$ and $\\varphi_n\\to\\infty$ as $n\\to\\infty$. Two timescale regimes are distinguished: a `fast' regime in which $\\varphi_n$ is superlinear and a `slow' regime in which $\\varphi_n$ is sublinear. We provide the exact asymptotics of $\\xi_n(u)$ (as $n\\to\\infty$) for both regimes, relying on change-of-measure arguments in combination with Edgew"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02999","kind":"arxiv","version":4},"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":"1801.02999","created_at":"2026-05-17T23:52:08.156287+00:00"},{"alias_kind":"arxiv_version","alias_value":"1801.02999v4","created_at":"2026-05-17T23:52:08.156287+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02999","created_at":"2026-05-17T23:52:08.156287+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZND7GZPJPJOF","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZND7GZPJPJOFOXKV","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZND7GZPJ","created_at":"2026-05-18T12:33:07.085635+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/ZND7GZPJPJOFOXKVHEFAV7HJ4G","json":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G.json","graph_json":"https://pith.science/api/pith-number/ZND7GZPJPJOFOXKVHEFAV7HJ4G/graph.json","events_json":"https://pith.science/api/pith-number/ZND7GZPJPJOFOXKVHEFAV7HJ4G/events.json","paper":"https://pith.science/paper/ZND7GZPJ"},"agent_actions":{"view_html":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G","download_json":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G.json","view_paper":"https://pith.science/paper/ZND7GZPJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1801.02999&json=true","fetch_graph":"https://pith.science/api/pith-number/ZND7GZPJPJOFOXKVHEFAV7HJ4G/graph.json","fetch_events":"https://pith.science/api/pith-number/ZND7GZPJPJOFOXKVHEFAV7HJ4G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G/action/storage_attestation","attest_author":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G/action/author_attestation","sign_citation":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G/action/citation_signature","submit_replication":"https://pith.science/pith/ZND7GZPJPJOFOXKVHEFAV7HJ4G/action/replication_record"}},"created_at":"2026-05-17T23:52:08.156287+00:00","updated_at":"2026-05-17T23:52:08.156287+00:00"}