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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…
Regularly varying stochastic processes are able to model extremal dependence between process values at locations in random fields. We investigate the empirical extremogram as an estimator of dependence in the extremes. We provide conditions…
Recursive max-linear vectors provide models for causal dependence between large values of random variables that are supported on directed acyclic graphs, but the standard assumption that all nodes of such a graph are observed can be…
We reconsider a classical, well-studied problem from applied probability. This is the max-sum equivalence of randomly weighted sums, and the originality is because we manage to include interdependence among the primary random variables, as…
We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…
Multiple metrics have been developed to detect causality relations between data describing the elements constituting complex systems, all of them considering their evolution through time. Here we propose a metric able to detect causality…
Determining the causes of extreme events is a fundamental question in many scientific fields. An important aspect when modelling multivariate extremes is the tail dependence. In application, the extreme dependence structure may…
The statistics of records in sequences of independent, identically distributed random variables is a classic subject of study. One of the earliest results concerns the stochastic independence of record events. Recently, records statistics…
We define a new multivariate time series model by generalizing the ARMAX process in a multivariate way. We give conditions on stationarity and analyze local dependence and domains of attraction. As a consequence of the obtained result, we…
The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…
Different dependence scenarios can arise in multivariate extremes, entailing careful selection of an appropriate class of models. In bivariate extremes, the variables are either asymptotically dependent or are asymptotically independent.…
Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with…
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…
The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…
We give an overview of several aspects arising in the statistical analysis of extreme risks with actuarial applications in view. In particular it is demonstrated that empirical process theory is a very powerful tool, both for the asymptotic…
Even though strongly correlated systems are abundant, only a few exceptional cases admit analytical solutions. In this paper we present a large class of solvable systems with strong correlations.. We consider a set of $N$ independent and…
In this paper, we propose a new aperiodic formulation of model predictive control for nonlinear continuous-time systems. Unlike earlier approaches, we provide event-triggered conditions without using the optimal cost as a Lyapunov function…
We consider a stationary stochastic volatility field $Y_vZ_v$ with $v\in\mathbb{Z}^d$, where $Z$ is regularly varying and $Y$ has lighter tails and is independent of $Z$. We make - relative to existing literature - very general assumptions…
Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying…
Extreme events are often multivariate in nature. A compound extreme occurs when a combination of variables jointly produces a significant impact, even if individual components are not necessarily marginally extreme. Compound extremes have…