Invariance properties of extremal cluster processes

This project introduces the general notion of a cluster process as a limiting point process of returns of a certain event in a time series, with a special focus on extremes. Under mild stationarity assumptions of the underlying time series the limiting process has certain invariance properties. Of particular interest are the cluster size distributions, where one needs to distinguish between a typical and inspected cluster sizes, which differ in their properties. As a central result of this project we derive a kind of "inspection paradox" for extremal clusters.