Related papers: Extremes and regular variation
Being the limits of copulas of componentwise maxima in independent random samples, extreme-value copulas can be considered to provide appropriate models for the dependence structure between rare events. Extreme-value copulas not only arise…
Fluctuations of global additive quantities, like total energy or magnetization for instance, can in principle be described by statistics of sums of (possibly correlated) random variables. Yet, it turns out that extreme values (the largest…
Motivated by the increasing availability of data of functional nature, we develop a general probabilistic and statistical framework for extremes of regularly varying random elements $X$ in $L^2[0,1]$. We place ourselves in a…
In a wide variety of situations, anomalies in the behaviour of a complex system, whose health is monitored through the observation of a random vector X = (X1,. .. , X d) valued in R d , correspond to the simultaneous occurrence of extreme…
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…
We investigate extreme value theory for physical systems with a global conservation law which describe renewal processes, mass transport models and long-range interacting spin models. As shown previously, a special feature is that the…
We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. The unifying theme is the Popa groups of our title viewed as locally…
The univariate extreme value theory deals with the convergence in type of powers of elements of sequences of cumulative distribution functions on the real line when the power index gets infinite. In terms of convergence of random variables,…
In this sequel to arXiv1407.4089 by the second author, we extend to multi-dimensional (or infinite-dimensional) settings the Goldie equation arising in the general regular variation of `General regular variation, Popa groups and quantifier…
We study analytically and numerically the extreme value distribution of observables defined along the temporal evolution of a dynamical system. The convergence to the Gumbel law of observable recurrences gives information on the fractal…
We investigate extreme value theory of a class of random sequences defined by the all-time suprema of aggregated self-similar Gaussian processes with trend. This study is motivated by its potential applications in various areas and its…
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 main objective of this paper is to develop extreme value theory for $\vartheta$-expansions. We establish the limit distribution of the maximum value in a $\vartheta$-continued fraction mixing stationary stochastic process, along with…
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…
Our contribution is to widen the scope of extreme value analysis applied to discrete-valued data. Extreme values of a random variable $X$ are commonly modeled using the generalized Pareto distribution, a method that often gives good results…
In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme…
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…
Analysis of the rare and extreme values through statistical modeling is an important issue in economical crises, climate forecasting, and risk management of financial portfolios. Extreme value theory provides the probability models needed…
We re-consider Leadbetter's extremal index for stationary sequences. It has interpretation as reciprocal of the expected size of an extremal cluster above high thresholds. We focus on heavy-tailed time series, in particular on regularly…
In this article we show the relationship between the Pareto distribution and the gamma distribution. This shows that the second one, appropriately extended, explains some anomalies that arise in the practical use of extreme value theory.…