{"paper":{"title":"On the tail asymptotics of the area swept under the Brownian storage graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Krzysztof D\\c{e}bicki, Marek Arendarczyk, Michel Mandjes","submitted_at":"2014-03-07T06:32:29Z","abstract_excerpt":"In this paper, the area swept under the workload graph is analyzed: with $\\{Q(t) : t\\ge0\\}$ denoting the stationary workload process, the asymptotic behavior of \\[\\pi_{T(u)}(u):={\\mathbb{P}}\\biggl(\\int_0^ {T(u)}Q(r)\\,\\mathrm{d}r>u\\biggr)\\] is analyzed. Focusing on regulated Brownian motion, first the exact asymptotics of $\\pi_{T(u)}(u)$ are given for the case that $T(u)$ grows slower than $\\sqrt{u}$, and then logarithmic asymptotics for (i) $T(u)=T\\sqrt{u}$ (relying on sample-path large deviations), and (ii) $\\sqrt{u}=\\mathrm{o}(T(u))$ but $T(u)=\\mathrm{o}(u)$. Finally, the Laplace transform o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.1665","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"}