Related papers: Weak dependence and optimal quantitative self-norm…

This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with $N$ samples can be linked to the $N$-particle…

Let (Zn) be a branching process with immigration in an independent and identically distributed random environment. Under necessary moment conditions, we show the exact convergence rate in the central limit theorem on logZn by using the…

There has been a resurgence of interest in incomplete U-statistics that only sum over a subset of kernel evaluations, due to their computational efficiency and asymptotic normality which can be leveraged to quantify the uncertainty of…

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in…

We develop novel empirical Bernstein inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of…

We consider Gaussian Laplace eigenfunctions on the two-dimensional flat torus (arithmetic random waves), and provide explicit Berry-Esseen bounds in the 1-Wasserstein distance for the normal and non-normal high-energy approximation of the…

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…

It is known that a random walk on $\Z^d$ among i.i.d. uniformly elliptic random bond conductances verifies a central limit theorem. It is also known that approximations of the covariance matrix can be obtained by considering periodic…

We consider eigenvalues of generalized Wishart processes as well as particle systems, of which the empirical measures converge to deterministic measures as the dimension goes to infinity. In this paper, we obtain central limit theorems to…

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…

We derive new bounds of the remainder in a combinatorial central limit theorem without assumptions on independence and existence of moments of summands. For independent random variables our theorems imply Esseen and Berry-Esseen type…

We obtain various new limit theorems for random walks on SL_2(C) under low moment conditions. For non-elementary measures with a finite second moment, we prove a Local Limit Theorem for the norm cocycle, yielding the optimal version of a…

Let $(Z_n)$ be a supercritical branching process in a random environment $\xi = (\xi_n)$. We establish a Berry-Esseen bound and a Cram\'er's type large deviation expansion for $\log Z_n$ under the annealed law $\mathbb P$. We also improve…

A new Berry-Esseen bound for non-linear functionals of non-symmetric and non-homogeneous infinite Rademacher sequences is established. It is based on a discrete version of the Malliavin-Stein method and an analysis of the discrete…

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 a general Berry-Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the general bound with Palm theory, we deduce a new error bound for assessing the accuracy of…

We establish nonuniform Berry-Esseen bounds for martingales under the conditional Bernstein condition. These bounds imply Cram\'er type large deviations for moderate $x$'s, and are of exponential decay rate as de la Pe\~na's inequality when…

We present the first minimax risk bounds for estimators of the spectral measure in multivariate linear factor models, where observations are linear combinations of regularly varying latent factors. Non-asymptotic convergence rates are…

In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain Burgers' equation and the stochastic reaction-diffusion equation. The weak…

A powerful robust mean estimator introduced by Catoni (2012) allows for mean estimation of heavy-tailed data while achieving the performance characteristics of classical mean estimator for sub-Gaussian data. While Catoni's framework has…