Multivariate extreme values for dynamical systems

TL;DR

This paper develops a theoretical framework for analyzing the dependence of extreme values in multivariate dynamical systems, combining spatial and temporal dependencies, with applications to specific systems.

Contribution

It introduces conditions tailored to dynamical systems for studying multivariate extreme value dependence, expanding the understanding of extreme events in complex systems.

Findings

Established conditions for multivariate extreme value dependence in dynamical systems

Analyzed cross-sectional dependence combining spatial and temporal factors

Provided illustrative applications with concrete systems and dependence sources

Abstract

We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of $\R^d$-valued observables evaluated along the orbits of the systems. We study this cross-sectional dependence, which results from the combination of a spatial and a temporal dependence structures. We give several illustrative applications, where concrete systems and dependence sources are introduced and analysed.