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Optimal Exact Simulation of Max-Stable and Related Random Fields | Zhipeng Liu
; Jose H. Blanchet
; A.B. Dieker
; Thomas Mikosch
; | Date: |
20 Sep 2016 | Abstract: | We consider the random field M(t)=sup_{ngeq 1}ig{-log
A_{n}+X_{n}(t)ig},,qquad tin T, for a set $Tsubset mathbb{R}^{m}$,
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 $cleft( d
ight) =c({t_{1},ldots,t_{d}})$ function
evaluations to sample $X_{n}$ at $d$ locations $t_{1},ldots ,t_{d}in T$. We
provide an algorithm which, for any $epsilon >0$, samples $M(t_{1}),ldots
,M(t_{d})$ with complexity $o(c(d),d^{epsilon })$. 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 $O(1/(delta log
(1/delta ))^{1/alpha })$, where $alpha $ relates to the H"{o}lder
continuity exponent of the process $X_{n}$ (so, if $X_{n}$ is Brownian motion,
$alpha =1/2$). | Source: | arXiv, 1609.6001 | Services: | Forum | Review | PDF | Favorites |
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