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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 $t_{1},\\ldots ,t_{d}\\in T$. 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