Related papers: On mean central limit theorems for stationary sequ…
In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.
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…
In this paper, we provide a central limit theorem for the finite-dimensional marginal distributions of empirical processes $(Z_n(f))_{f\in\mathcal{F}}$ whose index set $\mathcal{F}$ is a family of cluster functionals valued on blocks of…
We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally established for their marginal empirical…
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.
We provide explicit bounds on the Wasserstein distance between discrete time martingales and the standard normal distribution. The proofs are based on a combination of Lindeberg's and Stein's method.
We establish a central limit theorem and an invariance principle for stationary random fields, with projective-type conditions. Our result is obtained via an m-dependent approximation method. As applications, we establish invariance…
We give a general local central limit theorem for the sum of two independent random variables, one of which satisfies a central limit theorem while the other satisfies a local central limit theorem with the same order variance. We apply…
Consider the random walk $G_n : = g_n \ldots g_1$, $n \geq 1$, where $(g_n)_{n\geq 1}$ is a sequence of independent and identically distributed random elements with law $\mu$ on the general linear group ${\rm GL}(V)$ with $V=\mathbb R^d$.…
A strictly stationary sequence of random variables is constructed with the following properties: (i) the random variables take the values -1 and +1 with probability 1/2 each, (ii) every five of the random variables are independent, (iii)…
Multivariate distributions are explored using the joint distributions of marginal sample quantiles. Limit theory for the mean of a function of order statistics is presented. The results include a multivariate central limit theorem and a…
We consider the problem of finding, for a given quadratic measure of non-uniformity of a set of $N$ points (such as $L_2$ star-discrepancy or diaphony), the asymptotic distribution of this discrepancy for truly random points in the limit…
In this article, we study the smallest gaps of the Gaussian orthogonal ensemble. The main result is that the smallest gaps, after normalized by $n$, will tend to a Poisson distribution, and the limiting density of the $k$-th normalized…
The Central Limit Theorem states that, in the limit of a large number of terms, an appropriately scaled sum of independent random variables yields another random variable whose probability distribution tends to a stable distribution. The…
The limiting behavior of Toeplitz type quadratic forms of stationary processes has received much attention through decades, particularly due to its importance in statistical estimation of the spectrum. In the present paper we study such…
Let $f$ be a nonincreasing function defined on $[0,1]$. Under standard regularity conditions, we derive the asymptotic distribution of the supremum norm of the difference between $f$ and its Grenander-type estimator on sub-intervals of…
We give a new proof of the classical Central Limit Theorem, in the Mallows ($L^r$-Wasserstein) distance. Our proof is elementary in the sense that it does not require complex analysis, but rather makes use of a simple subadditive inequality…
Suppose that $X$ is a subcritical superprocess. Under some asymptotic conditions on the mean semigroup of $X$, we prove the Yaglom limit of $X$ exists and identify all quasi-stationary distributions of $X$.
The main result of this paper is a general central limit theorem for distributions defined by certain renewal type equations. We apply this to weakly self-avoiding random walks. We give good error estimates and Gaussian tail estimates which…
In this paper, on the sublinear expectation space, we establish a comparison theorem between independent and convolutionary random vectors, which states that the partial sums of those two sequences of random vectors are identically…