Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

TL;DR

This paper extends extreme value theory to non-stationary processes from sequential and random dynamical systems, relaxing previous mixing assumptions and providing detailed examples.

Contribution

It generalizes the theory of extreme values for non-stationary processes, especially for non-autonomous and random dynamical systems, with weaker mixing conditions.

Findings

Extended extreme value laws to non-stationary processes

Applied results to sequential and random dynamical systems

Provided detailed examples and case studies

Abstract

We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical systems, in particular to {\em sequential dynamical systems}, given by uniformly expanding maps, and to a few classes of random dynamical systems. Some examples are presented and worked out in detail.