• Bernoulli
  • Volume 24, Number 2 (2018), 1497-1530.

Exact and fast simulation of max-stable processes on a compact set using the normalized spectral representation

Marco Oesting, Martin Schlather, and Chen Zhou

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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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Bernoulli, Volume 24, Number 2 (2018), 1497-1530.

Received: March 2014
Revised: September 2016
First available in Project Euclid: 21 September 2017

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importance sampling mixed moving maxima optimal simulation


Oesting, Marco; Schlather, Martin; Zhou, Chen. Exact and fast simulation of max-stable processes on a compact set using the normalized spectral representation. Bernoulli 24 (2018), no. 2, 1497--1530. doi:10.3150/16-BEJ905.

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