{"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"}