Multivariate extreme values for dynamical systems

Romain Aimino; Ana Cristina Moreira Freitas; Jorge Milhazes Freitas; Mike Todd

doi:10.1088/1361-6544/ae36db

Multivariate extreme values for dynamical systems

Romain Aimino
, Ana Cristina Moreira Freitas
, Jorge Milhazes Freitas^*
, Mike Todd

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	015023
Number of pages	24
Journal	Nonlinearity
Volume	39
Issue number	1
DOIs	https://doi.org/10.1088/1361-6544/ae36db
Publication status	Published - 22 Jan 2026

Keywords

Multivariate extremes
Copulas
Extremal index

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Aimino_2026_Nonlinearity_Multivariate-extreme-values-dynamical-systems_CC
© 2026 The Author(s). Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license (https://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
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title = "Multivariate extreme values for dynamical systems",

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 ℝd-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.",

keywords = "Multivariate extremes, Copulas, Extremal index",

author = "Romain Aimino and Freitas, \{Ana Cristina Moreira\} and Freitas, \{Jorge Milhazes\} and Mike Todd",

note = "Funding: All authors were partially financed by Portuguese public funds through FCT—Funda{\c c}ao para a Ciencia e a Tecnologia, I.P., in the framework of the projects PTDC/MAT-PUR/4048/2021, 2022.07167.PTDC and CMUP{\textquoteright}s project with reference UIDB/00144/2020.",

year = "2026",

month = jan,

day = "22",

doi = "10.1088/1361-6544/ae36db",

language = "English",

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T1 - Multivariate extreme values for dynamical systems

AU - Aimino, Romain

AU - Freitas, Ana Cristina Moreira

AU - Freitas, Jorge Milhazes

AU - Todd, Mike

N1 - Funding: All authors were partially financed by Portuguese public funds through FCT—Fundaçao para a Ciencia e a Tecnologia, I.P., in the framework of the projects PTDC/MAT-PUR/4048/2021, 2022.07167.PTDC and CMUP’s project with reference UIDB/00144/2020.

PY - 2026/1/22

Y1 - 2026/1/22

N2 - 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 ℝd-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.

AB - 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 ℝd-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.

KW - Multivariate extremes

KW - Copulas

KW - Extremal index

U2 - 10.1088/1361-6544/ae36db

DO - 10.1088/1361-6544/ae36db

M3 - Article

SN - 0951-7715

VL - 39

JO - Nonlinearity

JF - Nonlinearity

IS - 1

M1 - 015023

ER -

Multivariate extreme values for dynamical systems

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