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Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…

Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…

Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…

In environmental science applications, extreme events frequently exhibit a complex spatio-temporal structure, which is difficult to describe flexibly and estimate in a computationally efficient way using state-of-art parametric…

This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…

We give conditions to prove the existence of an Extremal Index for general stationary stochastic processes by detecting the presence of one or more underlying periodic phenomena. This theory, besides giving general useful tools to identify…

Models for extreme values accommodating non-stationarity have been amply studied and evaluated from a parametric perspective. Whilst these models are flexible, in the sense that many parametrizations can be explored, they assume an…

A geometric representation for multivariate extremes, based on the shapes of scaled sample clouds in light-tailed margins and their so-called limit sets, has recently been shown to connect several existing extremal dependence concepts.…

Modelling and forecasting the occurrence of extreme events is especially difficult when the event process is nonstationary, with changes in both the rate at which extremes occur and the magnitude of the extremes when they occur. We approach…

We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localisation of energy, this system exhibits extreme events in the sense that individual elements of the chain show…

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- direct cascading or fragmentation, spatial dynamics, and external driving -- are combined in a classical age-dependent…

A central area of research in nonlinear science is the study of instabilities that drive the emergence of extreme events. Unfortunately, experimental techniques for measuring such phenomena often provide only partial characterization. For…

We consider discrete time dynamical systems and show the link between Hitting Time Statistics (the distribution of the first time points land in asymptotically small sets) and Extreme Value Theory (distribution properties of the partial…

We study the statistics of the maximum and minimum of a set of $N$ random variables whose dynamical and statistical properties fall within the scope of infinite ergodic theory. These non-stationary yet recurrent systems are described, in…

Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types…

Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…

We propose a framework for studying predictability of extreme events in complex systems. Major conceptual elements -- hierarchical structure, spatial dynamics, and external driving -- are combined in a classical branching diffusion with…

In this work, we report the emergence of extreme events in a damped and driven velocity-dependent mechanical system. We observe that the extreme events emerge at multiple points. We further notice that the extreme events occur symmetrically…

Machine Learning (ML) inspired algorithms provide a flexible set of tools for analyzing and forecasting chaotic dynamical systems. We here analyze the performance of one algorithm for the prediction of extreme events in the two-dimensional…

Graphical models in extremes have emerged as a diverse and quickly expanding research area in extremal dependence modeling. They allow for parsimonious statistical methodology and are particularly suited for enforcing sparsity in…