Related papers: Central limit theorem for triangular arrays of Non…

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…

A consistent kernel estimator of the limiting spectral distribution of general sample covariance matrices was introduced in Jing, Pan, Shao and Zhou (2010). The central limit theorem of the kernel estimator is proved in this paper.

The main objective of this paper is to establish bootstrap uniform functional central limit theorem for Harris recurrent Markov chains over uniformly bounded classes of functions. We show that the result can be generalized also to the…

Establishing central limit theorems (CLTs) for ergodic averages of Markov chains is a fundamental problem in probability and its applications. Since the seminal work~\cite{MR834478}, a vast literature has emerged on the sufficient…

This paper concerns with mesh restrictions that are needed to satisfy several important mathematical properties -- maximum principles, comparison principles, and the non-negative constraint -- for a general linear second-order elliptic…

We prove a central limit theorem for the length of the longest subsequence of a random permutation which follows one of a class of repeating patterns. This class includes every fixed pattern of ups and downs having at least one of each,…

In this paper, we give rates of convergence, for minimal distances and for the uniform distance, between the law of partial sums of martingale differences and thelimiting Gaussian distribution. More precisely, denoting by $P_{X}$ the law of…

In this paper, we establish novel concentration inequalities for additive functionals of geometrically ergodic Markov chains similar to Rosenthal inequalities for sums of independent random variables. We pay special attention to the…

We study cosmological polytopes induced by Erd\H{o}s--R\'enyi random graphs in a high-dimensional regime. These graph-based lattice polytopes form a natural model of random lattice polytopes in which geometric features are determined by the…

In this paper, we obtain an explicit total variation bound in the central limit theorem for the sums of non-i.i.d. random variables. Our results show that, under suitable assumptions, Lindeberg's condition is sufficient and necessary for…

We prove central limit theorems, Berry-Esseen type theorems, almost sure invariance principles, large deviations and Livsic type regularity for partial sums of the form $S_n=\sum_{j=0}^{n-1}f_j(...,X_{j-1},X_j,X_{j+1},...)$, where $(X_j)$…

We prove a Central Limit Theorem for the linear statistics of two-dimensional Coulomb gases, with arbitrary inverse temperature and general confining potential, at the macroscopic and mesoscopic scales and possibly near the boundary of the…

An isotropic fractional Brownian field (with Hurst parameter $H<1/2$) is observed in a family of points in the unit square $\mathbf{C}=(-1/2,1/2]^{2}$% . These points are assumed to come from a realization of a homogeneous Poisson point…

We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…

This paper provides a Central Limit Theorem (CLT) for a process $\{\theta_n, n\geq 0\}$ satisfying a stochastic approximation (SA) equation of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H(\theta_n,X_{n+1})$; a CLT for the associated…

We consider a sequence of Markov chains weakly convergent to a diffusion. We suppose that a drift term contains a linearly increasing component. The usual parametrix method fails because of this unbounded drift term. We show how to modify…

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,…

This paper extends classical probabilistic results to the broader class of demimartingales and demisubmartingales. We establish variants of Doob's-type optional sampling theorem under minimal structural conditions on stopping times, relying…

This paper will provide several classes of strictly stationary, countable-state, irreducible, aperiodic Markov chains that are reversible and have finite second moments, such that the central limit theorem fails to hold. The main purpose is…

We develop a general approach of the almost sure central limit theorem for the quasi-continuous vectorial martingales and we release a quadratic extension of this theorem while specifying speeds of convergence. As an application of this…