相关论文: Free extreme values

We solve two continuous extremal problems on the classes of monotone functions: in the first problem we find extremal values for a line integral of a coordinate-wise monotone function of two variables from a rearrange\-ment-invariant class…

This paper is concerned with the limit theory of the extreme order statistics derived from random walks. We establish the joint convergence of the order statistics near the minimum of a random walk in terms of the Feller chains. Detailed…

We show that the distribution of self-normalized sums of free self-adjoint random variables converges weakly to Wigner's semicircle law under appropriate conditions and estimate the rate of convergence in terms of the Kolmogorov distance.…

Situations in many fields of research, such as digital communications, nuclear physics and mathematical finance, can be modelled with random matrices. When the matrices get large, free probability theory is an invaluable tool for describing…

We derive theorems which outline explicit mechanisms by which anomalous scaling for the probability density function of the sum of many correlated random variables asymptotically prevails. The results characterize general anomalous scaling…

Classical methods for quantile regression fail in cases where the quantile of interest is extreme and only few or no training data points exceed it. Asymptotic results from extreme value theory can be used to extrapolate beyond the range of…

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

The possibilities of the use of the coefficient of variation over a high threshold in tail modelling are discussed. The paper also considers multiple threshold tests for a generalized Pareto distribution, together with a threshold selection…

Extreme values of real phenomena are events that occur with low frequency, but can have a large impact on real life. These are, in many practical problems, high-dimensional by nature (e.g. Tawn, 1990; Coles and Tawn, 1991). To study these…

An overview of existing nonparametric tests of extreme-value dependence is presented. Given an i.i.d.\ sample of random vectors from a continuous distribution, such tests aim at assessing whether the underlying unknown copula is of the {\em…

It is well known that the distribution of extreme values of strictly stationary sequences differ from those of independent and identically distributed sequences in that extremal clustering may occur. Here we consider non-stationary but…

We prove a law of large numbers in terms of complete convergence of independent random variables taking values in increments of monotone functions, with convergence uniform both in the initial and the final time. The result holds also for…

A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…

The classical approach to multivariate extreme value modelling assumes that the joint distribution belongs to a multivariate domain of attraction. This requires each marginal distribution be individually attracted to a univariate extreme…

Consider a random sample from a bivariate distribution function $F$ in the max-domain of attraction of an extreme-value distribution function $G$. This $G$ is characterized by two extreme-value indices and a spectral measure, the latter…

We explore the dependence structure in the sampled sequence of large networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like…

The Poincar\'e algebra can be extended (non-centrally) to the Maxwell algebra and beyond. These extensions are relevant for describing particle dynamics in electro-magnetic backgrounds and possibly including the backreaction due the…

Max-stable processes are increasingly widely used for modelling complex extreme events, but existing fitting methods are computationally demanding, limiting applications to a few dozen variables. $r$-Pareto processes are mathematically…

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…

The phenomenon of superconvergence is proved for all freely infinitely divisible distributions. Precisely, suppose that the partial sums of a sequence of free identically distributed, infinitesimal random variables converge in distribution…