Related papers: A Sharp Gaussian Tail Bound for Sums of Uniforms

Under K.-T. Sturm's formulation, we obtain a Gaussian upper bound for tail probability of mean value of independent, identically distributed random variables with values in $\mathbb{R}$-trees and Hadamard manifolds.

We take an $L_1$-dense class of functions $\Cal F$ on a measurable space $(X,\Cal X)$ together with a sequence of independent, identically distributed $X$-space valued random variables $\xi_1,\dots,\xi_n$ and give a good estimate on the…

This is the first part of a series of papers devoted to studying the right tail profile of a bulk Gaussian multiplicative chaos measure with uniform singularity on the boundary. We investigate the bulk/boundary quotients of Gaussian…

In this paper, we compute multivariate tail risk probabilities where the marginal risks are heavy-tailed and the dependence structure is a Gaussian copula. The marginal heavy-tailed risks are modeled using regular variation which leads to a…

Let $\{X_1, X_2, ... \}$ be a sequence of dependent heavy-tailed random variables with distributions $F_1, F_2,...$ on $(-\infty,\infty)$, and let $\tau$ be a nonnegative integer-valued random variable independent of the sequence $\{X_k, k…

We estimate up to universal constants tails of symmetric and totally asymmetric 1-dimensional $\alpha$-stable distributions in terms of functions of the parameters of these distributions. In particular, for values of $\alpha$ close to $2$…

Let $\{\xi_1,\xi_2,\ldots\}$ be a sequence of independent but not necessarily identically distributed random variables. In this paper, the sufficient conditions are found under which the tail probability…

A well-known longstanding conjecture on the supremum of the tails of normalized sums of independent Rademacher random variables is disproved. A related conjecture, also recently disproved, is discussed.

We deduce in this paper the sufficient conditions for weak convergence of centered and normed deviation of the u-statistics with values in the space of the real valued continuous function defined on some compact metric space. We obtain also…

We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.

An infinite convergent sum of independent and identically distributed random variables discounted by a multiplicative random walk is called perpetuity, because of a possible actuarial application. We give three disjoint groups of sufficient…

Let $\{\xi_n\}$ be a sequence of independent and identically distributed random variables. In this paper we study the comparison for two upper tail probabilities $\mathbb{P}\{\sum_{n=1}^{\infty}a_n|\xi_n|^p\geq r\}$ and…

This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy property. We then give a connection…

We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $\sum_{Nt\geq n\geq…

We consider the problem of finding the optimal upper bound for the tail probability of a sum of $k$ nonnegative, independent and identically distributed random variables with given mean $x$. For $k=1$ the answer is given by Markov's…

We study the tail asymptotics of the sum of two heavy-tailed random variables. The dependence structure is modeled by copulas with the so-called tail order property. Examples are presented to illustrate the approach. Further for each…

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level…

We extend a result of Goldreich and Ron about estimating the collision probability of a hash function. Their estimate has a polynomial tail. We prove that when the load factor is greater than a certain constant, the estimator has a gaussian…

Several objects in the Extremes literature are special instances of max-stable random sup-measures. This perspective opens connections to the theory of random sets and the theory of risk measures and makes it possible to extend…

We consider the tail behavior of random variables $R$ which are solutions of the distributional equation $R\stackrel{d}{=}Q+MR$, where $(Q,M)$ is independent of $R$ and $|M|\le 1$. Goldie and Gr\"{u}bel showed that the tails of $R$ are no…