An Introduction to Functional Extreme Value Theory

Abstract

The extension of D-norms to functional spaces in Section 1.10 provides a smooth approach to functional extreme value theory, in particular to generalized Pareto processes and max-stable processes. Multivariate max-stable dfs were introduced in Section 2.3 by means of generalized Pareto distributions. We repeat this approach and introduce max-stable processes via generalized Pareto processes. In Section 4.3, we show how to generate max-stable processes via SMS rvs. This approach, which generalizes the max-linear model established by Wang and Stoev (2011), entails the prediction of max-stable processes in space, not in time. The Brown–Resnick process is a prominent example.