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≥ 1 {− log An+ Xn (t)}, t∈ T, for a set T⊂ Rm, where (Xn) is an iid sequence of centered Gaussian random fields on T and 0< A1< A2 0, samples M (t1),..., M (td) with complexity o (c (d) dϵ) as measured in the Lp norm sense for any p≥ 1. Moreover, if Xn has an as converging series representation, then M can be as approximated with error δ uniformly over T and with complexity O (1/(δ log (1/δ)) 1/α), where α relates to the Hölder continuity exponent of the process Xn (so, if Xn is Brownian motion, α= 1/2).

Authors
ZHIPENG LIU, JOSE BLANCHET, AB DIEKER, THOMAS MIKOSCH
Publication date
2017/8/30