Related papers: Decoupling Inequalities for the Tail Probabilities…

In this paper, we will give a sufficient condition for a non-negative random variable $X$ to be heavy tailed by investigating the Laplace-Stieltjes transform of the probability distribution function. We focus on the relation between the…

We present a method for upper and lower bounding the right and the left tail probabilities of continuous random variables (RVs). For the right tail probability of RV $X$ with probability density function $f (x)$, this method requires first…

We consider the sums $S_n=\xi_1+\cdots+\xi_n$ of independent identically distributed random variables. We do not assume that the $\xi$'s have a finite mean. Under subexponential type conditions on distribution of the summands, we find the…

In 2017-2020 Jordanova and co-authors investigate probabilities for p-outside values and determine them in many particular cases. They show that these probabilities are closely related to the concept for heavy tails. Tukey's boxplots are…

In this paper, we present a new framework to obtain tail inequalities for sums of random matrices. Compared with existing works, our tail inequalities have the following characteristics: 1) high feasibility--they can be used to study the…

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…

We generalize a famous tail Doob's inequality, relative two non-negative random variables, arising in the martingale theory, in two directions: on the more general source data and on the random variables belonging to the so-called Grand…

We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…

Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…

Let $X$ be an integrable discrete random variable over $\{0, 1, 2, \ldots\}$ with $\mathbb{P}(X = i + 1) \leq \mathbb{P}(X = i)$ for all $i$. Then for any integer $a \geq 1$, $\mathbb{P}(X \leq a) \leq \mathbb{E}[X] / (2a - 1)$. Let $W$ be…

We obtain an asymptotic expansion for the tails of the random variable $\tcal=\arg\max_{u\in\mathbb{R}}(\mathcal{A}_2(u)-u^2)$ where $\mathcal{A}_2$ is the Airy$_2$ process. Using the formula of Schehr \cite{Sch} that connects the density…

This paper investigates the relationship between various measure-theoretic properties of U-statistics with fixed sample size $N$ and the same properties of their kernels. Specifically, the random variables are replaced with elements in some…

Let $X_1,\dots,X_n$ be independent normal random variables with $X_i\sim N(\mu_i,\sigma_i^2)$, and set $Z=\prod_{i=1}^n X_i$. We derive asymptotic approximations for the right tail probability $\mathbb{P}(Z>x)$ as $x\to\infty$. When at…

In this paper we present a method for obtaining tail-bounds for random variables satisfying certain probabilistic recurrences that arise in the analysis of randomized parallel divide and conquer algorithms. In such algorithms, some…

We present moment inequalities for completely degenerate Banach space valued (generalized) U-statistics of arbitrary order. The estimates involve suprema of empirical processes which, in the real-valued case, can be replaced by simpler…

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a…

We formulate a uniform tail bound for empirical processes indexed by a class of functions, in terms of the individual deviations of the functions rather than the worst-case deviation in the considered class. The tail bound is established by…

The non-asymptotic tail bounds of random variables play crucial roles in probability, statistics, and machine learning. Despite much success in developing upper bounds on tail probability in literature, the lower bounds on tail…

The paper presents an efficient method for simulating the tails of a target variable Z=h(X) which depends on a set of basic variables X=(X_1, ..., X_n). To this aim, variables X_i, i=1, ..., n are sequentially simulated in such a manner…

We characterize the UMD property of a Banach space by tail inequalities for maximal functions of tangent conditionally symmetric processes. More precisely, we prove that a Banach space $V$ is UMD if and only if for some (equivalently, for…