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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Max–Stable Processes: Representations, Ergodic Properties and Statistical Applications
verfasst von : Stilian A. Stoev
Erschienen in: Dependence in Probability and Statistics
Verlag: Springer Berlin Heidelberg
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Max-stable processes arise as limits in distribution of component-wise maxima of independent processes, under suitable centering and normalization. Therefore, the class of max-stable processes plays a central role in the study and modeling of extreme value phenomena. This chapter starts with a review of classical and some recent results on the representations of max-stable processes. Recent results on necessary and sufficient conditions for the ergodicity and mixing of stationary max-stable processes are then presented. These results readily yield the consistency of many statistics for max-stable processes. As an example, a new estimator of the extremal index for a stationary max-stable process is introduced and shown to be consistent.