相关论文: Elementary Proofs of the Main Limit Theorems of Pr…

A central limit theorem for arrays of symmetric row-wise exchangeable random variables is presented. The result is valid for finite and infinite extendable and non-extendable sequences. Unlike most reported versions of the central limit…

We prove weak laws of large numbers and central limit theorems of Lindeberg type for empirical centres of mass (empirical Fr\'echet means) of independent non-identically distributed random variables taking values in Riemannian manifolds. In…

Let $L_{n}$ be the least common multiple of a random set of integers obtained from $\{1,\ldots,n\}$ by retaining each element with probability $\theta\in (0,1)$ independently of the others. We prove that the process $(\log L_{\lfloor…

We prove a central limit theorem with aassumptions which are many weak than classical conditions

Frequentists' inference often delivers point estimators associated with confidence intervals or sets for parameters of interest. Constructing the confidence intervals or sets requires understanding the sampling distributions of the point…

Randomness is a central concept to statistics and physics. Here, a statistical analysis shows experimental evidence that tossing coins and finding last digits of prime numbers are identical regarding statistics for equally likely outcomes.…

Kolmogorov's exponential inequalities are basic tools for studying the strong limit theorems such as the classical laws of the iterated logarithm for both independent and dependent random variables. This paper establishes the Kolmogorov…

We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…

A function from sequences to their subsequences is called selection function. A selection function is called admissible (with respect to normal numbers) if for all normal numbers, their subsequences obtained by the selection function are…

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance, expressed through lower and upper expectations. The results are variants and extensions of De Cooman and Miranda's recent…

We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We extend…

We establish some limit theorems for quasi-arithmetic means of random variables. This class of means contains the arithmetic, geometric and harmonic means. Our feature is that the generators of quasi-arithmetic means are allowed to be…

We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that…

We prove an almost sure weak limit theorem for simple linear rank statistics for samples with continuous distributions functions. As a corollary the result extends to samples with ties, and the vector version of an a.s. central limit…

The theory of random matrices contains many central limit theorems. We have central limit theorems for eigenvalues statistics, for the log-determinant and log-permanent, for limiting distribution of individual eigenvalues in the bulk, and…

We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…

In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.

Peng (2006) initiated a new kind of central limit theorem under sub-linear expectations. Song (2017) gave an estimate of the rate of convergence of Peng's central limit theorem. Based on these results, we establish a new kind of almost sure…

We study the convergence in distribution norms in the Central Limit Theorem for non identical distributed random variables that is $$ \varepsilon_{n}(f):={\mathbb{E}}\Big(f\Big(\frac 1{\sqrt…

Every sequence $f_1, f_2, \cdots \, $ of random variables with $ \, \lim_{M \to \infty} \big( M \sup_{k \in \mathbb{N}} \mathbb{P} ( |f_k| > M ) \big)=0\,$ contains a subsequence $ f_{k_1}, f_{k_2} , \cdots \,$ that satisfies, along with…