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.
"A Comparative Tour through the Simulation Algorithms for Max-Stable Processes." Statist. Sci. 37 (1) 42 - 63, February 2022. https://doi.org/10.1214/20-STS820