{"paper":{"title":"Extremes of independent stochastic processes: a point process approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Cl\\'ement Dombry (LMA), Fr\\'ed\\'eric Eyi-Minko (LMA)","submitted_at":"2011-09-28T13:55:41Z","abstract_excerpt":"For each $n\\geq 1$, let $ {X_{in}, \\quad i \\geq 1} $ be independent copies of a nonnegative continuous stochastic process $X_{n}=(X_n(t))_{t\\in T}$ indexed by a compact metric space $T$. We are interested in the process of partial maxima [\\tilde M_n(u,t) =\\max \\{X_{in}(t), 1 \\leq i\\leq [nu]},\\quad u\\geq 0,\\ t\\in T.] where the brackets $[\\,\\cdot\\,]$ denote the integer part. Under a regular variation condition on the sequence of processes $X_n$, we prove that the partial maxima process $\\tilde M_n$ weakly converges to a superextremal process $\\tilde M$ as $n\\to\\infty$. We use a point process app"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6209","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"}