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- W2972967637 abstract "We consider the random field begin{equation*}M(t)=mathop{mathrm{sup}}_{ngeq1}{-log A_{n}+X_{n}(t)},qquad tin T,end{equation*} for a set $Tsubsetmathbb{R}^{m}$, where $(X_{n})$ is an i.i.d. 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 $c(d)=c({t_{1},ldots,t_{d}})$ function evaluations to sample $X_{n}$ at $d$ locations $t_{1},ldots,t_{d}in T$. We provide an algorithm which samples $M(t_{1}),ldots,M(t_{d})$ with complexity $O(c(d)^{1+o(1)})$ as measured in the $L_{p}$ norm sense for any $pge1$. Moreover, if $X_{n}$ has an a.s. converging series representation, then $M$ can be a.s. approximated with error $delta$ uniformly over $T$ and with complexity $O(1/(deltalog(1/delta))^{1/alpha})$, where $alpha$ relates to the Hölder continuity exponent of the process $X_{n}$ (so, if $X_{n}$ is Brownian motion, $alpha=1/2$)." @default.
- W2972967637 created "2019-09-19" @default.
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- W2972967637 date "2019-11-01" @default.
- W2972967637 modified "2023-10-17" @default.
- W2972967637 title "On logarithmically optimal exact simulation of max-stable and related random fields on a compact set" @default.
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- W2972967637 doi "https://doi.org/10.3150/18-bej1076" @default.
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