A comparative tour through the simulation algorithms for max-stable processes

TL;DR

This paper reviews and compares various simulation algorithms for max-stable processes, which are crucial for analyzing extreme events in space and time, highlighting their properties and theoretical foundations.

Contribution

It provides a comprehensive overview and theoretical comparison of existing simulation methods for max-stable processes, enhancing understanding of their relative advantages.

Findings

Different algorithms have distinct efficiency and accuracy profiles.

Theoretical results help clarify the conditions under which each method performs best.

The overview guides future research and practical application in spatial risk assessment.

Abstract

Being the max-analogue of $\alpha$-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 spatio-temporal 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.