Related papers: Tail processes for stable-regenerative multiple-st…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
We study the empirical version of halfspace depths with the objective of establishing a connection between the rates of convergence and the tail behaviour of the corresponding underlying distributions. The intricate interplay between the…
In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical…
Modern risk modelling approaches deal with vectors of multiple components. The components could be, for example, returns of financial instruments or losses within an insurance portfolio concerning different lines of business. One of the…
We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but…
We develop a novel characterization of extremal dependence between two cortical regions of the brain when its signals display extremely large amplitudes. We show that connectivity in the tails of the distribution reveals unique features of…
This study aims to develop the limit theorems on the sample autocovariances and sample autocorrelations for certain stationary infinitely divisible processes. We consider the case where the infinitely divisible process has heavy tail…
Inference over tails is usually performed by fitting an appropriate limiting distribution over observations that exceed a fixed threshold. However, the choice of such threshold is critical and can affect the inferential results. Extreme…
We consider a system consisting of a sequential composition of Mealy machines, called head and tail. We study two problems related to these systems. In the first problem, models of both head and tail components are available, and the aim is…
The classical modeling of spatial extremes relies on asymptotic models (i.e., max-stable processes or $r$-Pareto processes) for block maxima or peaks over high thresholds, respectively. However, at finite levels, empirical evidence often…
We propose a transformation capable of altering the tail properties of a distribution, motivated by extreme value theory, which can be used as a layer in a normalizing flow to approximate multivariate heavy tailed distributions. We apply…
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…
The linear switching system is a system of ODE with the time-dependent matrix taking values from a given control matrix set. The system is (asymptotically) stable if all its trajectories tend to zero for every control function. We consider…
To consider a high-dimensional random process, we propose a notion about stochastic tensor-valued random process (TRP). In this work, we first attempt to apply a generic chaining method to derive tail bounds for all p-th moments of the…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted…
We consider a stationary regularly varying time series which can be expressedas a function of a geometrically ergodic Markov chain. We obtain practical conditionsfor the weak convergence of the tail array sums and feasible estimators…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
Diffusion models have emerged as powerful generative frameworks with widespread applications across machine learning and artificial intelligence systems. While current research has predominantly focused on linear diffusions, these…
We study the formation of high energy tails in a one-dimensional kinetic model for granular gases, the so-called Inelastic Maxwell Model. We introduce a time- discretized version of the stochastic process, and show that continuous time…