Liu, Z., Blanchet, J. H., Dieker, A. B., & Mikosch, T. (2016). On Optimal Exact Simulation of Max-Stable and Related Random Fields. ArXiv. /abs/1609.06001

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Abstract

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 , where is an iid 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, for any , samples with complexity . 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 H\"{o}lder continuity exponent of the process (so, if is Brownian motion, ).

Authors
Zhipeng Liu, Jose H Blanchet, AB Dieker, Thomas Mikosch
Publication date
2016/9/20
Journal
arXiv preprint arXiv:1609.06001