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Exact and fast simulation of max-stable processes on a compact set using the normalized spectral representation. (English) Zbl 1431.60042
Authors’ abstract: 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.

MSC:
60G70 Extreme value theory; extremal stochastic processes
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60G20 Generalized stochastic processes
62-08 Computational methods for problems pertaining to statistics
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