Related papers: Some notes on moment inequalities for heavy-tailed…

We consider a new approach in the definition of two-dimensional heavy-tailed distributions. Namely, we introduce the classes of two-dimensional long-tailed, of twodimensional dominatedly varying and of two-dimensional consistently varying…

Science in the 21st century seems to be governed by novel approaches involving interdisciplinary work, systemic perspectives and complexity theory concepts. These new paradigms force us to leave aside our elder mechanistic approaches and…

Consider a critical branching random walk on $\mathbb{Z}^d$, $d\geq 1$, started with a single particle at the origin, and let $L(x)$ be the total number of particles that ever visit a vertex $x$. We study the tail of $L(x)$ under suitable…

We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…

In this paper we define the class of matrix Mittag-Leffler distributions and study some of its properties. We show that it can be interpreted as a particular case of an inhomogeneous phase-type distribution with random scaling factor, and…

We derive two-sided estimates on moments and tails of Gaussian chaoses, that is, random variables of the form $\sum a_{i_1,...,i_d}g_{i_1}... g_{i_d}$, where $g_i$ are i.i.d. ${\mathcal{N}}(0,1)$ r.v.'s. Estimates are exact up to constants…

We present explicit estimates of right and left tails and exact (up to universal, multiplicative constants) estimates of tails and moments of hitting times of Bessel processes. The latter estimates are obtained from more general estimates…

It is argued that there is a need for fat-tailed distributions that become thin in the extreme tail. A 3-parameter distribution is introduced that visually resembles the t-distribution and interpolates between the normal distribution and…

We extend the theory of concentration inequalities to simple random tensors with heavy-tailed coefficients. Specifically, we consider the class of sub-Weibull distributions $\mathcal{S}_\alpha$ for $\alpha \in [1, 2]$. We establish…

Understanding the shape of a distribution of data is of interest to people in a great variety of fields, as it may affect the types of algorithms used for that data. We study one such problem in the framework of distribution property…

Given an arbitrary continuous probability density function, it is introduced a conjugated probability density, which is defined through the Shannon information associated with its cumulative distribution function. These new densities are…

Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…

We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss various subclasses and the relation between them. To characterize…

We establish the one-to one bilateral interrelations between an asymptotic behavior for the tail of distributions for random variables and its great moments evaluation. Our results generalize the famous Richter's ones.

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.…

Stable subordinators, and more general subordinators possessing power law probability tails, have been widely used in the context of subdiffusions, where particles get trapped or immobile in a number of time periods, called constant…

This paper addresses the problem of estimating the tail index of distributions with heavy, Pareto-type tails for dependent data, that is of interest in the areas of finance, insurance, environmental monitoring and teletraffic analysis. A…

We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…

We obtain decay rates of probabilities of tails of polynomials in several independent random variables with heavy tails and derive stable limit theorems for nonconventional sums of such polynomials

If a random variable is not exponentially integrable, it is known that no concentration inequality holds for an infinite sequence of independent copies. Under mild conditions, we establish concentration inequalities for finite sequences of…