Related papers: Extremal Index, Hitting Time Statistics and period…
We present a comprehensive investigation of $\epsilon$-entropy, $h(\epsilon)$, in dynamical systems, stochastic processes and turbulence. Particular emphasis is devoted on a recently proposed approach to the calculation of the…
The extremal index parameter theta characterizes the degree of local dependence in the extremes of a stationary time series and has important applications in a number of areas, such as hydrology, telecommunications, finance and…
In this article there is no intention to repeat basic concepts about risk management, but we will try to define why often is usefull the time series analysis during the assessment of risks, and how is possible to compute a significative…
Extreme value analysis is an essential methodology in the study of rare and extreme events, which hold significant interest in various fields, particularly in the context of environmental sciences. Models that employ the exceedances of…
Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase--space. In this…
This study provides a summary of the theory which enables the analysis of extreme values, i.e., of measurements acquired from the observation of extraordinary/rare physical phenomena. The formalism is developed in a transparent way,…
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and…
Extreme events, such as rogue waves, earthquakes and stock market crashes, occur spontaneously in many dynamical systems. Because of their usually adverse consequences, quantification, prediction and mitigation of extreme events are highly…
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…
The asymptotic results that underlie applications of extreme random fields often assume that the variables are located on a regular discrete grid, identified with $\mathbb{Z}^2$, and that they satisfy stationarity and isotropy conditions.…
Estimation of extreme conditional quantiles is often required for risk assessment of natural hazards in climate and geo-environmental sciences and for quantitative risk management in statistical finance, econometrics, and actuarial…
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…
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…
This article introduces the class of periodic trawl processes, which are continuous-time, infinitely divisible, stationary stochastic processes, that allow for periodicity and flexible forms of their serial correlation, including both…
This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of…
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…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
Modern statistical analyses often encounter datasets with massive sizes and heavy-tailed distributions. For datasets with massive sizes, traditional estimation methods can hardly be used to estimate the extreme value index directly. To…
The analysis of spatial extremes requires the joint modeling of a spatial process at a large number of stations and max-stable processes have been developed as a class of stochastic processes suitable for studying spatial extremes. Spatial…
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…