Related papers: Stable central limit theorems for discrete-time la…

In this paper, we obtain stability results for martingale representations in a very general framework. More specifically, we consider a sequence of martingales each adapted to its own filtration, and a sequence of random variables…

We present a general methodology to construct triplewise independent sequences of random variables having a common but arbitrary marginal distribution $F$ (satisfying very mild conditions). For two specific sequences, we obtain in closed…

In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…

In this article, we fill a gap in the literature on Hawkes processes. In particular, we derive a CLT for a non linear compound marked Hawkes process. We also provide an upper bound on the convergence rate using the functional 1-Wasserstein…

We prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in the one-dimensional lattice with variable diffusion coefficient. The scaling limits are obtained from a similar…

We study central limit theorems for certain nonlinear sequences of random variables. In particular, we prove the central limit theorems for the bounded conductivity of the random resistor networks on hierarchical lattices.

The paper presents a methodology for temporal logic verification of continuous-time switched stochastic systems. Our goal is to find the lower bound on the probability that a complex temporal property is satisfied over a finite time…

In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…

We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and concentration of measure. Unlike Skorokhod…

This is an expository review paper elaborating on the proof of the martingale functional central limit theorem (FCLT). This paper also reviews tightness and stochastic boundedness, highlighting one-dimensional criteria for tightness used in…

In this paper, we rigorously derive Central Limit Theorems (CLT) for Bayesian two-layerneural networks in the infinite-width limit and trained by variational inference on a regression task. The different networks are trained via different…

We establish a practical and easy-to-implement sequential stopping rule for the martingale central limit theorem, focusing on Monte Carlo methods for estimating the mean of a non-iid sequence of martingale difference type. Starting with an…

The intent of this paper is to describe the large scale asymptotic geometry of iteration stable (STIT) tessellations in $\mathbb{R}^d$, which form a rather new, rich and flexible class of random tessellations considered in stochastic…

Using Bernstein polynomial approximations, we prove the central limit theorem for linear spectral statistics of sample covariance matrices, indexed by a set of functions with continuous fourth order derivatives on an open interval including…

The central limit theorem (CLT) is one of the most fundamental results in probability; and establishing its rate of convergence has been a key question since the 1940s. For independent random variables, a series of recent works established…

We consider two classical ensembles of the random matrix theory: the Wigner matrices and sample covariance matrices, and prove Central Limit Theorem for linear eigenvalue statistics under rather weak (comparing with results known before)…

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…

Recently, the fundamental lemma by Willems et al. has been extended towards stochastic LTI systems subject to process disturbances. Using this lemma requires previously recorded data of inputs, outputs, and disturbances. In this paper, we…

When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…

Concept Drift (CD) detection intends to continuously identify changes in data stream behaviors, supporting researchers in the study and modeling of real-world phenomena. Motivated by the lack of learning guarantees in current CD algorithms,…