The Generalized Pareto process; with application

In extreme value statistics the peaks-over-threshold method is widely used. The method is based on the Generalized Pareto distribution ([1], [8] in univariate theory and e.g. [3], [14] in multivariate theory) characterizing probabilities of exceedances over high thresholds. We present a generalization of this concept in the space of continuous functions. We call this the Generalized Pareto process. Different from earlier papers our definition is not based on a distribution function but on functional properties. As an application we use the theory to produce wind fields connected to disastrous storms on the basis of observed extreme but not disastrous storms.