Related papers: Clustering of high values in random fields
The extremal index is an important parameter in the characterization of extreme values of a stationary sequence. Our new estimation approach for this parameter is based on the extremal behavior under the local dependence condition…
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…
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…
The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces…
This paper investigates the asymptotic behavior of the extremes of a sequence of generalized Oppenheim random variables. Particularly, we establish conditions under which some normalized extremes of sequences arising from Oppenheim…
Extreme events over large spatial domains may exhibit highly heterogeneous tail dependence characteristics, yet most existing spatial extremes models yield only one dependence class over the entire spatial domain. To accurately characterize…
Let $\{Z(\tau,s), (\tau,s)\in [a,b]\times[0,T]\}$ with some positive constants $a,b,T$ be a centered Gaussian random field with variance function $\sigma^{2}(\tau,s)$ satisfying $\sigma^{2}(\tau,s)=\sigma^{2}(\tau)$. We firstly derive the…
Observing a load process above high thresholds, modeling it as a pulse process with random occurrence times and magnitudes, and extrapolating life-time maximum or design loads from the data is a common task in structural reliability…
Motivated by the papers of Piterbarg (2004) and H\"{u}sler (2004), in this paper the asymptotic relation between the maximum of a continuous dependent homogeneous Gaussian random field and the maximum of this field sampled at discrete time…
We establish sharp tail asymptotics for component-wise extreme values of bivariate Gaussian random vectors with arbitrary correlation between the components. We consider two scaling regimes for the tail event in which we demonstrate the…
Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…
A commonly used characteristic of statistical dependence of adjacency relations in real networks, the clustering coefficient, evaluates chances that two neighbours of a given vertex are adjacent. An extension is obtained by considering…
These notes were written for the mini-course "Extrema of log-correlated random variables: Principles and Examples" at the Introductory School held in January 2015 at the Centre International de Rencontres Math\'ematiques in Marseille. There…
We introduce the concept of geometric extremal graphical models, which are defined through the gauge function of the limit set obtained from suitably scaled random vectors in light-tailed margins. For block graphs, we prove results relating…
In this paper, we investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and…
The risk of catastrophes is related to the possibility of occurring extreme values. Several statistical methodologies have been developed in order to evaluate the propensity of a process for the occurrence of high values and the permanence…
We establish a connection between the structure of a stationary symmetric alpha-stable random field (0 < alpha < 2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosinski (2000). With the help of this…
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…
Motivated by examples from extreme value theory we introduce the general notion of a cluster process as a limiting point process of returns of a certain event in a time series. We explore general invariance properties of cluster processes…
In this paper we examine isotropic Gaussian random fields defined on $\mathbb R^N$ satisfying certain conditions. Specifically, we investigate the type of a critical point situated within a small vicinity of another critical point, with…