{"paper":{"title":"Extremes of Order Statistics of Stationary Processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.OT"],"primary_cat":"math.PR","authors_text":"Chengxiu Ling, Enkelejd Hashorva, Krzysztof Debicki, Lanpeng Ji","submitted_at":"2014-03-28T12:10:34Z","abstract_excerpt":"Let $\\{X_i(t),t\\ge0\\}, 1\\le i\\le n$ be independent copies of a stationary process $\\{X(t), t\\ge0\\}$. For given positive constants $u,T$, define the set of $r$th conjunctions $ C_{r,T,u}:= \\{t\\in [0,T]: X_{r:n}(t) > u\\}$ with $X_{r:n}(t)$ the $r$th largest order statistics of $X_1(t), \\ldots , X_n(t), t\\ge 0$. In numerous applications such as brain mapping and digital communication systems, of interest is the approximation of the probability that the set of conjunctions $C_{r,T,u}$ is not empty. Imposing the Albin's conditions on $X$, in this paper we obtain an exact asymptotic expansion of thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7354","kind":"arxiv","version":2},"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"}