The efficiency of simulation algorithms for max-stable processes relies on the choice of the spectral representation: different choices result in different sequences of finite approximations to the process.We propose a constructive approach yielding a normalized spectral representation that solves an optimization problem related to the efficiency of simulating max-stable processes. The simulation algorithm based on the normalized spectral representation can be regarded as max-importance sampling. Compared to other simulation algorithms hitherto, our approach has at least two advantages. First, it allows the exact simulation of a comprising class of max-stable processes. Second, the algorithm has a stopping time with finite expectation. In practice, our approach has the potential of considerably reducing the simulation time of max-stable processes.

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Keywords Importance sampling, Mixed moving maxima, Optimal simulation
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Journal Bernoulli
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Oesting, M. (Marco), Schlather, M, & Zhou, C. (Chen). (2018). Exact and fast simulation of max-stable processes on a compact set using the normalized spectral representation. Bernoulli, 24(2), 1497–1530. doi:10.3150/16-BEJ905