Zhipeng Liu. Jose H. Blanchet. A.B. Dieker. Thomas Mikosch. “On logarithmically optimal exact simulation of max-stable and related random fields on a compact set.” Bernoulli 25 (4A) 2949 – 2981, November 2019. https://doi.org/10.3150/18-BEJ1076
Abstract
We consider the random field \begin{equation*}M(t)=\mathop{\mathrm{sup}}_{n\geq1}\{-\log A_{n}+X_{n}(t)\},\qquad t\in T,\end{equation*} for a set , where is an i.i.d. sequence of centered Gaussian random fields on and are the arrivals of a general renewal process on , independent of . In particular, a large class of max-stable random fields with Gumbel marginals have such a representation. Assume that one needs function evaluations to sample at locations . We provide an algorithm which samples with complexity as measured in the norm sense for any . Moreover, if has an a.s. converging series representation, then can be a.s. approximated with error uniformly over and with complexity , where relates to the Hölder continuity exponent of the process (so, if is Brownian …
Authors
Zhipeng Liu, Jose H Blanchet, ANTONIUS B Dieker, Thomas Mikosch
Publication date
2019/11/1
Volume
25
Issue
4A
Pages
2949-2981
