{"paper":{"title":"Extremes of order statistics of self-similar processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chengxiu Ling","submitted_at":"2014-12-12T10:01:06Z","abstract_excerpt":"Let $\\{X_i(t),t\\ge0\\}, 1\\le i\\le n$ be independent copies of a random process $\\{X(t), t\\ge0\\}$. For a given positive constant $u$, define the set of $r$th conjunctions $C_r(u):=\\{t\\in[0,1]: X_{r:n}(t)>u\\}$ with $ X_{r:n}$ the $r$th largest order statistics of $X_i, 1\\le i\\le n$. In numerical applications such as brain mapping and digital communication systems, of interest is the approximation of $p_r(u)=\\mathbb P\\{C_r(u)\\neq\\phi\\}$. Instead of stationary processes dealt with by D\\c{e}bicki et al. (2014), we consider in this paper $X$ a self-similar $\\mathbb R$-valued process with $P$-continuo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3934","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"}