{"paper":{"title":"On Optimal Exact Simulation of Max-Stable and Related Random Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A.B. Dieker, Jose H. Blanchet, Thomas Mikosch, Zhipeng Liu","submitted_at":"2016-09-20T02:52:42Z","abstract_excerpt":"We consider the random field M(t)=\\sup_{n\\geq 1}\\big\\{-\\log A_{n}+X_{n}(t)\\big\\}\\,,\\qquad t\\in T\\, for a set $T\\subset \\mathbb{R}^{m}$, where $(X_{n})$ is an iid sequence of centered Gaussian random fields on $T$ and $0<A_{1}<A_{2}<\\cdots $ are the arrivals of a general renewal process on $(0,\\infty )$, independent of $(X_{n})$. In particular, a large class of max-stable random fields with Gumbel marginals have such a representation. Assume that one needs $c\\left( d\\right) =c(\\{t_{1},\\ldots,t_{d}\\})$ function evaluations to sample $X_{n}$ at $d$ locations $t_{1},\\ldots ,t_{d}\\in T$. We provide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06001","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"}