Multivariate extreme values for dynamical systems
Dynamical Systems
2026-01-21 v3 Probability
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 -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.
Cite
@article{arxiv.2406.14807,
title = {Multivariate extreme values for dynamical systems},
author = {Romain Aimino and Ana Cristina Moreira Freitas and Jorge Milhazes Freitas and Mike Todd},
journal= {arXiv preprint arXiv:2406.14807},
year = {2026}
}
Comments
Added an appendix and revised some parts to improve readability. To appear in Nonlinearity