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Brown-Resnick processes are max-stable processes that are associated toGaussian processes. Their simulation is often based on the correspondingspectral representation which is not unique. We study to what extent simulationaccuracy and efficiency can be improved by minimizing the maximal variance ofthe underlying Gaussian process. Such a minimization is a difficultmathematical problem that also depends on the geometry of the simulationdomain. We extend Matheron's (1974) seminal contribution in two aspects: (i)making his description of a minimal maximal variance explicit for convexvariograms on symmetric domains and (ii) proving that the same strategy reducesthe maximal variance also for a huge class of non-convex variogramsrepresentable through a Bernstein function. A simulation study confirms thatour non-costly modification can lead to substantial improvements among Gaussianrepresentations. We also compare it with three other established algorithms.

Efficient simulation of Brown-Resnick processes based on variance reduction of Gaussian processes