Related papers: Multiple Extremal Integrals
Extremality and irreducibility constitute fundamental concepts in mathematics, particularly within tropical geometry. While extremal decomposition is typically computationally hard, this article presents a fast algorithm for identifying the…
We give necessary and sufficient conditions for two sub-vectors of a random vector with a multivariate extreme value distribution, corresponding to the limit distribution of the maximum of a multidimensional stationary sequence with…
This paper introduces a comprehensive framework for complex-valued probability measures and explores their novel applications in information theory and statistical analysis. We define a complex probability measure as a phase-modulated…
Extreme events are often multivariate in nature. A compound extreme occurs when a combination of variables jointly produces a significant impact, even if individual components are not necessarily marginally extreme. Compound extremes have…
This article is devoted to the study of tail index estimation based on i.i.d. multivariate observations, drawn from a standard heavy-tailed distribution, i.e. of which 1-d Pareto-like marginals share the same tail index. A multivariate…
The classical multivariate extreme value theory tries to capture the extremal dependence between the components under a multivariate domain of attraction condition and it requires each of the components to be in the domain of attraction of…
We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector.…
Extremal length is a classical tool in 1-dimensional complex analysis for building conformal invariants. We propose a higher-dimensional generalization for complex manifolds and provide some ideas on how to estimate and calculate it. We…
Currently available models for spatial extremes suffer either from inflexibility in the dependence structures that they can capture, lack of scalability to high dimensions, or in most cases, both of these. We present an approach to spatial…
The quantitative analysis of financial time series often reveals two distinct features that standard Gaussian frameworks fail to capture: heavy-tailed marginal distributions and the phenomenon of extreme co-movements.While extreme value…
We suggest approximating the distribution of the sum of independent and identically distributed random variables with a Pareto-like tail by combining extreme value approximations for the largest summands with a normal approximation for the…
We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…
Leveraging the recently emerging geometric approach to multivariate extremes and the flexibility of normalising flows on the hypersphere, we propose a principled deep-learning-based methodology that enables accurate joint tail extrapolation…
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 concept of univariate Range Value-at-Risk, presented by Cont et al. (2010), is extended in the multidimensional setting. Traditional risk measures are not well suited when dealing with heavy-tail distributions and infinite tail…
The core of the classical block maxima method consists of fitting an extreme value distribution to a sample of maxima over blocks extracted from an underlying series. In asymptotic theory, it is usually postulated that the block maxima are…
We develop a novel multi-factor copula model for multivariate spatial extremes, which is designed to capture the different combinations of marginal and cross-extremal dependence structures within and across different spatial random fields.…
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 $k$-means clustering algorithm and its variant, the spherical $k$-means clustering, are among the most important and popular methods in unsupervised learning and pattern detection. In this paper, we explore how the spherical $k$-means…
We study the extremal behavior of a stochastic integral driven by a multivariate L\'{e}vy process that is regularly varying with index $\alpha>0$. For predictable integrands with a finite $(\alpha+\delta)$-moment, for some $\delta>0$, we…