On Max-Semistable Laws and Extremes for Dynamical Systems.

Suppose (f,X,μ) is a measure preserving dynamical system and ϕ:X→R a measurable observable. Let Xi=ϕ∘fi-1 denote the time series of observations on the system, and consider the maxima process Mn:=max{X1,…,Xn}. Under linear scaling of Mn, its asymptotic statistics are usually captured by a three-parameter generalised extreme value distribution.