Memory effects in recurrent and extreme events.

A dynamical approach to recurrent and extreme events is developed focusing on the role of correlations and memory in the structure of the probability distributions and their low-order moments. The procedure is illustrated on homogeneous first and second order Markov chains, non-Markovian and nonhomogeneous processes and deterministic dynamical systems. Substantial differences with classical statistical theory as applied to independent identically distributed random variables are identified.