Related papers: Heavy-tailed Distributions In Stochastic Dynamical…
Despite the successes of probabilistic models based on passing noise through neural networks, recent work has identified that such methods often fail to capture tail behavior accurately, unless the tails of the base distribution are…
Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…
We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big-jump principle. The principle states that in the presence of stochastic processes…
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…
Recently, increasing empirical evidence indicates the extensive existence of heavy tails in the interevent time distributions of various human behaviors. Based on the queuing theory, the Barab\'asi model and its variations suggest the…
We consider a class of multiplicative processes which, added with stochastic reset events, give origin to stationary distributions with power-law tails -- ubiquitous in the statistics of social, economic, and ecological systems. Our main…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
We propose and analyze a new estimator of the covariance matrix that admits strong theoretical guarantees under weak assumptions on the underlying distribution, such as existence of moments of only low order. While estimation of covariance…
This work proposes a novel method to robustly and accurately model time series with heavy-tailed noise, in non-stationary scenarios. In many practical application time series have heavy-tailed noise that significantly impacts the…
We consider causal discovery in structural causal models driven by heavy-tailed noise, where extremes carry important information about causal direction. We introduce the Heavy-Tailed Homogeneous Structural Causal Model (HT-HSCM), a unified…
The paper focuses on a class of light-tailed multivariate probability distributions. These are obtained via a transformation of the margins from a heavy-tailed original distribution. This class was introduced in Balkema et al. (J.…
Networks with stochastic variables described by heavy tailed lognormal distribution are ubiquitous in nature, and hence they deserve an exact information-theoretic characterization. We derive analytical formulas for mutual information…
We introduce a stochastic model to explain a double power-law distribution which exhibits two different Paretian behaviors in the upper and the lower tail and widely exists in social and economic systems. The model incorporates fitness…
A model of homogeneously driven dissipative system, consisting of a collection of $N$ particles that are characterized by only their velocities, is considered. Adopting a discrete time dynamics, at each time step, a pair of velocities is…
In the study of heavy tail data, several models have been introduced. If the interest is in the tail of the distribution, block maxima or excess over thresholds are the typical approaches, wasting relevant information in the bulk of the…
Real space condensation is known to occur in stochastic models of mass transport in the regime in which the globally conserved mass density is greater than a critical value. It has been shown within models with factorised stationary states…
This paper investigates the asymptotic behavior of higher-order conditional tail moments, which quantify the contribution of individual losses in the event of systemic collapse. The study is conducted within a framework comprising two…
We analyse circumstances in which bifurcation-driven jumps in AI systems are associated with emergent heavy-tailed outcome distributions. By analysing how a control parameter's random fluctuations near a catastrophic threshold generate…
We study discrete statistical mechanics systems perturbed by a random environment without a finite second moment. Specifically, we consider a random environment whose tail distribution satisfies $P[\omega > x] \sim x^{-\gamma}$ as $x \to…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…