Open Access
November 2014 The generalized Pareto process; with a view towards application and simulation
Ana Ferreira, Laurens de Haan
Bernoulli 20(4): 1717-1737 (November 2014). DOI: 10.3150/13-BEJ538


In extreme value statistics, the peaks-over-threshold method is widely used. The method is based on the generalized Pareto distribution characterizing probabilities of exceedances over high thresholds in $\mathbb{R}^{d}$. We present a generalization of this concept in the space of continuous functions. We call this the generalized Pareto process. Differently from earlier papers, our definition is not based on a distribution function but on functional properties, and does not need a reference to a related max-stable process.

As an application, we use the theory to simulate wind fields connected to disastrous storms on the basis of observed extreme but not disastrous storms. We also establish the peaks-over-threshold approach in function space.


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Ana Ferreira. Laurens de Haan. "The generalized Pareto process; with a view towards application and simulation." Bernoulli 20 (4) 1717 - 1737, November 2014.


Published: November 2014
First available in Project Euclid: 19 September 2014

zbMATH: 1312.60068
MathSciNet: MR3263087
Digital Object Identifier: 10.3150/13-BEJ538

Keywords: domain of attraction , Extreme value theory , functional regular variation , generalized Pareto process , max-stable processes , peaks-over-threshold

Rights: Copyright © 2014 Bernoulli Society for Mathematical Statistics and Probability

Vol.20 • No. 4 • November 2014
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