Related papers: On a Berry-Esseen type limit theorem for Boolean c…
We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.
In this paper we prove the central limit theorem for the number of clusters formed by the particles of the Arratia flow starting from the interval $[0;n]$ as $n\to\infty$ and obtain an estimate of the Berry-Esseen type for the rate of this…
A Berry--Ess\'{e}en theorem for linear combinations of iterates of an inner function is obtained. Our proof, which is based an elementary transfer argument and classical results in martingale theory, also leads to a simple proof of Nicolau…
Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…
We investigate the convergence rate in the Lyapunov theorem when the third absolute moments exist. By means of convex analysis we obtain the sharp estimate for the distance in the mean metric between a probability distribution and its zero…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
We prove a Berry-Esseen bound in de Jong's classical CLT for normalized, completely degenerate $U$-statistics, which says that the convergence of the fourth moment sequence to three and a Lindeberg-Feller type negligibility condition are…
Homogeneous normalized random measures with independent increments (hNRMIs) represent a broad class of Bayesian nonparametric priors and thus are widely used. In this paper, we obtain the strong law of large numbers, the central limit…
In this note, we study possible extensions of the Central Limit Theorem for non-convex bodies. First, we prove a Berry-Esseen type theorem for a certain class of unconditional bodies that are not necessarily convex. Then, we consider a…
We develop a new quantitative approach to a multidimensional version of the well-known {\it de Jong's central limit theorem} under optimal conditions, stating that a sequence of Hoeffding degenerate $U$-statistics whose fourth cumulants…
This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…
We consider solutions of stochastic differential equations which diverge to infinity as the time parameter goes to infinity. If the coefficients converge as the spacial variable goes to infinity, then the solutions will get close to some…
As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically…
We revisit the central limit theorem for integrated periodograms, equivalently for Toeplitz quadratic forms of stationary Gaussian sequences. Under a regular-variation assumption allowing long-memory singularities and slowly varying…
We establish central limit theorems for a large class of supercritical branching Markov processes in infinite dimension with spatially dependent and non-necessarily local branching mechanisms. This result relies on a fourth moment…
We investigate the rate of convergence toward the Boolean extreme value distribution, which is the universal limiting law for the normalized spectral maximum of Boolean independent and identically distributed positive operators, under the…
We proof a limit theorem for moments in space of the increments of Brownian local time. As special cases for the second and third moments, previous results by Chen et al. (Ann. Prob. 38, 2010, no. 1) and Rosen (Stoch. Dyn. 11, 2011, no. 1),…
We provide bounds of Berry-Esseen type for fundamental limit theorems in operator-valued free probability theory such as the operator-valued free Central Limit Theorem and the asymptotic behaviour of distributions of operator-valued…
In this work, we provide a $(n/m)^{-1/2}$-rate finite sample Berry-Esseen bound for $m$-dependent high-dimensional random vectors over the class of hyper-rectangles. This bound imposes minimal assumptions on the random vectors such as…
In order to characterize the fluctuation between the ergodic limit and the time-averaging estimator of a full discretization in a quantitative way, we establish a central limit theorem for the full discretization of the parabolic stochastic…