  As an example for complex systems with extreme events we investigate ocean
wave states exhibiting rogue waves. We present a statistical method of data
analysis based on multi-point statistics which for the first time allows
grasping extreme rogue wave events in a statistically highly satisfactory
manner. The key to the success of the approach is mapping the complexity of
multi-point data onto the statistics of hierarchically ordered height
increments for different time scales for which we can show that a stochastic
cascade process with Markov properties is governed by a Fokker-Planck equation.
Conditional probabilities as well as the Fokker-Planck equation itself can be
estimated directly from the available observational data. With this stochastic
description surrogate data sets can in turn be generated allowing to work out
arbitrary statistical features of the complex sea state in general and extreme
rogue wave events in particular. The results also open up new perspectives for
forecasting the occurrence probability of extreme rogue wave events, and even
for forecasting the occurrence of individual rogue waves based on precursory
dynamics.
