Related papers: Representations of max-stable processes based on s…
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…
Dynamical systems with high intrinsic dimensionality are often characterized by extreme events having the form of rare transitions several standard deviations away from the mean. For such systems, order-reduction methods through projection…
It is often assumed that events cannot occur simultaneously when modelling data with point processes. This raises a problem as real-world data often contains synchronous observations due to aggregation or rounding, resulting from…
In spite of precautions to avoid the harmful effects of extreme events, we experience recurrently phenomena that overcome the preventive barriers. These barriers usually increase drastically right after the occurrence of such extreme…
In this paper, we discuss the emergence of extreme events in a parametrically driven non-polynomial mechanical system with a velocity-dependent potential. We confirm the occurrence of extreme events from the probability distribution…
This book provides a comprehensive introduction for the study of extreme events in the context of dynamical systems. The introduction provides a broad overview of the interdisciplinary research area of extreme events, underlining its…
Macroevolutionary dynamics often display sudden, explosive surges, where systems remain relatively stable for extended periods before experiencing dramatic acceleration that frequently exceeds traditional exponential growth. This pattern is…
The extremal index $\theta$, a measure of the degree of local dependence in the extremes of a stationary process, plays an important role in extreme value analyses. We estimate $\theta$ semiparametrically, using the relationship between the…
We propose a general framework to study last passage times, suprema and drawdowns of a large class of stochastic processes. A central role in our approach is played by processes of class Sigma. After investigating convergence properties and…
Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger…
This article summarises the methods used by the team ``Ca' Foscari" for the EVA 2025 Data Challenge. The questions of the challenge concern the estimation of exceedance probabilities across several locations. Rather than modelling the…
The extremal coefficient function (ECF) of a max-stable process $X$ on some index set $T$ assigns to each finite subset $A\subset T$ the effective number of independent random variables among the collection $\{X_t\}_{t\in A}$. We introduce…
When passing from the univariate to the multivariate setting, modelling extremes becomes much more intricate. In this introductory exposition, classical multivariate extreme value theory is presented from the point of view of multivariate…
We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there…
Problem definition: Data-driven models in machine learning have enabled efficient management of production systems. However, a majority of machine learning models are devoted to modeling the mean response or average pattern, which is…
This paper is devoted to the estimation of a vector $\bm {\theta}$ parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency and asymptotic normality results of this estimator…
Polycrystalline metal failure often begins with stress concentration at grain boundaries. Identifying which microstructural features trigger these events is important but challenging because these extreme damage events are rare and the…
Probabilistic reasoning systems combine different probabilistic rules and probabilistic facts to arrive at the desired probability values of consequences. In this paper we describe the MESA-algorithm (Maximum Entropy by Simulated Annealing)…
This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated supremum at a fixed time on the entire support of the joint…
Inference over tails is performed by applying only the results of extreme value theory. Whilst such theory is well defined and flexible enough in the univariate case, multivariate inferential methods often require the imposition of…