Related papers: A radial version of the Central Limit Theorem

We provide rates of convergence in the central limit theorem in terms of projective criteria for adapted stationary sequences of centered random variables taking values in Banach spaces, with finite moment of order $p \in ]2,3]$ as soon as…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

We define the local empirical process, based on $n$ i.i.d. random vectors in dimension $d$, in the neighborhood of the boundary of a fixed set. Under natural conditions on the shrinking neighborhood, we show that, for these local empirical…

In this article we formulate the CLT associated to Gaussian operators of type B -- see \cite{BEH15}, where important role is played by colored pair partitions. Then we present a certain family of noncommutative random matrix models for the…

For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$,…

We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems…

We prove a Central Limit Theorem for the empirical optimal transport cost, $\sqrt{\frac{nm}{n+m}}\{\mathcal{T}_c(P_n,Q_m)-\mathcal{T}_c(P,Q)\}$, in the semi discrete case, i.e when the distribution $P$ is supported in $N$ points, but…

Via a covariance representation based on characteristic functions, a known elementary proof of the Gaussian concentration inequality is presented. A few other applications are briefly mentioned.

We establish central limit theorems for the Sample Average Approximation (SAA) method in discrete-time, finite-horizon stochastic optimal control. Our analysis is based on an abstract limit theorem for stochastic backward recursions, which…

In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.

In this paper, we use the theory of symmetric Dirichlet forms to give a probabilistic interpretation of Calder\'{o}n's inverse conductivity problem in terms of reflecting diffusion processes and their corresponding boundary trace processes.

We study moderate deviations of suprema of parametrized sequences of sample bounded Gaussian processes $\{X _x(t), t\in T _x\}$, and first present recent sharp bounds in simple cases. In the almost periodic case, we prove an approximation…

This article presents a weak law of large numbers and a central limit theorem for the scaled realised covariation of a bivariate Brownian semistationary process. The novelty of our results lies in the fact that we derive the suitable…

Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

In this paper we show that the conditional distribution of perturbed chi-quare risks can be approximated by certain distributions including the Gaussian ones. Our results are of interest for conditional extreme value models and multivariate…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

In this note we consider the finite-dimensional parameter estimation problem associated to inverse problems. In such scenarios, one seeks to maximize the marginal likelihood associated to a Bayesian model. This latter model is connected to…

We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…

Central limit theorems play an important role in the study of statistical inference for stochastic processes. However, when the nonparametric local polynomial threshold estimator, especially local linear case, is employed to estimate the…