Related papers: Limit theorems for deviation means of independent …

We prove a multivariate central limit theorem with explicit error bound on a non-smooth function distance for sums of bounded decomposable $d$-dimensional random vectors. The decomposition structure is similar to that of Barbour, Karo\'nski…

This paper is concerned with Spearman's correlation matrices under large dimensional regime, in which the data dimension diverges to infinity proportionally with the sample size. We establish the central limit theorem for the linear…

We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…

In this paper we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix-variate location mixture of normal…

In the probability theory limit distributions (or probability measures) are often characterized by some convolution equations (factorization properties) rather than by Fourier transforms (the characteristic functionals). In fact, usually…

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…

We establish the central limit theorem for linear processes with dependent innovations including martingales and mixingale type of assumptions as defined in McLeish [Ann. Probab. 5 (1977) 616--621] and motivated by Gordin [Soviet Math.…

We establish a Law of Large Numbers and a Central Limit Theorem for a class of Crump Mode Jagers continuous time branching processes, where the birth rate is age dependent, and also random (different from one individual to the next), in the…

In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol,…

The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…

We consider supercritical branching random walks on transitive graphs and we prove a law of large numbers for the mean displacement of the ensemble of particles, and a Stam-type central limit theorem for the empirical distributions, thus…

We consider a family of positive operator valued measures associated with representations of compact connected Lie groups. For many independent copies of a single state and a tensor power representation we show that the observed probability…

Linear structural error-in-variables models with univariate observations are revisited for studying modified least squares estimators of the slope and intercept. New marginal central limit theorems (CLT's) are established for these…

We show central limit theorems (CLT) for the Stieltjes transforms or more general analytic functions of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of $\alpha$-stable laws and…

We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and H\"anggi ([DH1], [DH2]). We address here two questions,…

We consider the Grenander estimator that is the maximum likelihood estimator for non-increasing densities. We prove uniform central limit theorems for certain subclasses of bounded variation functions and for H\"older balls of smoothness…

We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…