• Corpus ID: 88513930

# Representations of max-stable processes based on single extreme events

@article{Engelke2012RepresentationsOM,
title={Representations of max-stable processes based on single extreme events},
author={Sebastian Engelke and Alexander Malinowski and Marco Oesting and Martin Schlather},
journal={arXiv: Probability},
year={2012}
}
• Published 11 September 2012
• Mathematics
• arXiv: Probability
This paper provides the basis for new methods of inference for max-stable processes \xi\ on general spaces that admit a certain incremental representation, which, in important cases, has a much simpler structure than the max-stable process itself. A corresponding peaks-over-threshold approach will incorporate all single events that are extreme in some sense and will therefore rely on a substantially larger amount of data in comparison to estimation procedures based on block maxima. Conditioning…
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## References

SHOWING 1-10 OF 27 REFERENCES

### MAX-STABLE PROCESSES AND SPATIAL EXTREMES

Max-stable processes arise from an infinite-dimensional generalisation of extreme value theory. They form a natural class of processes when sample maxima are observed at each site of a spatial

### On the structure and representations of max-stable processes

• Mathematics
Advances in Applied Probability
• 2010
We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles.

### Likelihood-Based Inference for Max-Stable Processes

• Mathematics
• 2009
The last decade has seen max-stable processes emerge as a common tool for the statistical modeling of spatial extremes. However, their application is complicated due to the unavailability of the

### Estimation of Hüsler–Reiss distributions and Brown–Resnick processes

• Mathematics
• 2012
Estimation of extreme value parameters from observations in the max‐domain of attraction of a multivariate max‐stable distribution commonly uses aggregated data such as block maxima. Multivariate

### Simulation of Brown–Resnick processes

• Mathematics
• 2012
Brown–Resnick processes form a flexible class of stationary max-stable processes based on Gaussian random fields. With regard to applications, fast and accurate simulation of these processes is an

### Spatial extremes: Models for the stationary case

• Mathematics
• 2006
The aim of this paper is to provide models for spatial extremes in the case of stationarity. The spatial dependence at extreme levels of a stationary process is modeled using an extension of the

### Joint extremal behavior of hidden and observable time series with applications to GARCH processes

• Mathematics
• 2011
For a class of generalized hidden Markov models (Xt,Yt)t∈ℤ$(X_{t},Y_{t})_{t \in \mathbb {Z}}$ we analyze the limiting behavior of the (suitably scaled) unobservable part (Yt)t∈ℤ\$(Y_{t})_{t\in \mathbb

### Stationary max-stable fields associated to negative definite functions.

• Mathematics
• 2009
Let Wi, i∈ℕ, be independent copies of a zero-mean Gaussian process {W(t), t∈ℝd} with stationary increments and variance σ2(t). Independently of Wi, let ∑i=1∞δUi be a Poisson point process on the real

### Multivariate Generalized Pareto Distributions

• Mathematics
• 2006
Statistical inference for extremes has been a subject of intensive research over the past couple of decades. One approach is based on modelling exceedances of a random variable over a high threshold