{"paper":{"title":"Logarithmic asymptotics for multidimensional extremes under non-linear scalings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Kamil Marcin Kosinski, Michel Mandjes","submitted_at":"2012-11-06T17:26:52Z","abstract_excerpt":"Let $\\boldsymbol W=\\{\\boldsymbol W_n:n\\in\\mathbb N\\}$ be a sequence of random vectors in $\\mathbb R^d$, $d\\ge 1$. This paper considers the logarithmic asymptotics of the extremes of $\\boldsymbol W$, that is, for any vector $\\boldsymbol q>\\boldsymbol 0$ in $\\mathbb R^d$, we find $$\\log\\mathbb P\\left(\\exists{n\\in\\mathbb N}:\\boldsymbol W_n> u \\boldsymbol q\\right), \\quad\\text{as} u\\to\\infty.$$ We follow the approach of the restricted large deviation principle introduced in Duffy et al. \\textit{Logarithmic asymptotics for the supremum of a stochastic process} (Ann. Appl. Probab., 13:430--445, 2003)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1318","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"}