Related papers: Systematic co-occurrence of tail correlation funct…
We are interested in investigating the statistical properties of extreme values for strongly correlated variables. The starting motivation is to understand how the strong-correlation properties of power-law distributed processes affect the…
There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…
Codifference is a commonly used measure of dependence for stable vectors and processes for which covariance is infinite. However, we argue that it can also be used for other heavy-tail distributions and it provides useful information for…
The Peaks-Over Threshold is a fundamental method in the estimation of rare events such as small exceedance probabilities, extreme quantiles and return periods. The main problem with the Peaks-Over Threshold method relates to the selection…
Identifying and quantifying spatial correlation are important aspects of studying the collective behaviour of multi-agent systems. Pair correlation functions (PCFs) are powerful statistical tools which can provide qualitative and…
Although inertial particle-laden flows occur in a wide range of industrial and natural processes, there is both a lack of fundamental understanding of these flows and continuum-level governing equations needed to predict transport and…
Multistable distributions, which have been introduced recently by Falconer, L\'evy V\'ehel and their co-authors, are natural generalizations of symmetric "alpha" stable distributions; roughly speaking, they are obtained by replacing the…
The set of infinite-dimensional, symmetric stable tail dependence functions associated with exchangeable max-stable sequences of random variables with unit Fr\'echet margins is shown to be a simplex. Except for a single element, the…
Correlation mixtures of elliptical copulas arise when the correlation parameter is driven itself by a latent random process. For such copulas, both penultimate and asymptotic tail dependence are much larger than for ordinary elliptical…
The t copula is often used in risk management as it allows for modelling tail dependence between risks and it is simple to simulate and calibrate. However, the use of a standard t copula is often criticized due to its restriction of having…
Archimedean copulas generated by Laplace transforms have been extensively studied in the literature, with much of the focus on tail dependence limited only to cases where the Laplace transforms exhibit regular variation with positive tail…
The key to successful statistical analysis of bivariate extreme events lies in flexible modelling of the tail dependence relationship between the two variables. In the extreme value theory literature, various techniques are available to…
The long-time behaviors of the velocity autocorrelation function (VACF) for granular flows based on the optimal velocity fluid model are investigated theoretically. It is found the long-time tail of VACF disappears in a granular flow under…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
An asymptotic model for extreme behavior of certain Markov chains is the "tail chain". Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this…
The tail measure of a regularly varying stationary time series has been recently introduced. It is used in this contribution to reconsider certain properties of the tail process and establish new ones. A new formulation of the time change…
In this paper we discuss the problem of the estimation of extreme event occurrence probability for data drawn from some multifractal process. We also study the heavy (power-law) tail behavior of probability density function associated with…
The tail chain of a Markov chain can be used to model the dependence between extreme observations. For a positive recurrent Markov chain, the tail chain aids in describing the limit of a sequence of point processes $\{N_n,n\geq1\}$,…
Copulas have become an important tool in the modern best practice Enterprise Risk Management, often supplanting other approaches to modelling stochastic dependence. However, choosing the `right' copula is not an easy task, and the…
Let $\{X_t, t \geq 1\}$ be a sequence of identically distributed and pairwise asymptotically independent random variables with regularly varying tails and $\{ \Theta_t, t\geq1 \}$ be a sequence of positive random variables independent of…