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February 2022 A Comparative Tour through the Simulation Algorithms for Max-Stable Processes
Marco Oesting, Kirstin Strokorb
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Statist. Sci. 37(1): 42-63 (February 2022). DOI: 10.1214/20-STS820


Being the max-analogue of α-stable stochastic processes, max-stable processes form one of the fundamental classes of stochastic processes. With the arrival of sufficient computational capabilities, they have become a benchmark in the analysis of spatiotemporal extreme events. Simulation is often a necessary part of inference of certain characteristics, in particular for future spatial risk assessment. In this article, we give an overview over existing procedures for this task, put them into perspective of one another and use some new theoretical results to make comparisons with respect to their properties.


The new theoretical results for this manuscript were obtained during mutual visits of KS at the University of Siegen and MO at Cardiff University. MO and KS thank their hosting institutions for their generous hospitality. The authors are also very grateful for the thoughtful suggestions from the reviewing process. In particular, these comments resulted in the clarification of the marginal standardization and the inclusion of Section 2. This substantial revision was undertaken during summer/autumn 2020. MO thankfully acknowledges financial support by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC 2075—390740016 at the University of Stuttgart.


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Marco Oesting. Kirstin Strokorb. "A Comparative Tour through the Simulation Algorithms for Max-Stable Processes." Statist. Sci. 37 (1) 42 - 63, February 2022.


Published: February 2022
First available in Project Euclid: 19 January 2022

MathSciNet: MR4372096
zbMATH: 07474197
Digital Object Identifier: 10.1214/20-STS820

Keywords: error assessment , extremal functions , ‎spectral representation , threshold stopping

Rights: Copyright © 2022 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2022
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