Max–Stable Processes: Representations, Ergodic Properties and Statistical Applications

Abstract

AbstractMax-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.KeywordsSpectral FunctionStable ProcessBorel FunctionStrong ConsistencyPoisson Point ProcessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.