Related papers: Central Limit Theorems for Stochastic Approximatio…

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…

Let $(X_i)$ be a stationary and ergodic Markov chain with kernel $Q$, $f$ an $L^2$ function on its state space. If $Q$ is a normal operator and $f = (I-Q)^{1/2}g$ (which is equivalent to the convergence of $\sum_{n=1}^\infty…

In this paper we study the functional central limit theorem for stationary Markov chains with self-adjoint operator and general state space. We investigate the case when the variance of the partial sum is not asymptotically linear in n; and…

Mean field games (MFGs) describe the limit, as $n$ tends to infinity, of stochastic differential games with $n$ players interacting with one another through their common empirical distribution. Under suitable smoothness assumptions that…

Central limit theorems (CLTs) have a long history in probability and statistics. They play a fundamental role in constructing valid statistical inference procedures. Over the last century, various techniques have been developed in…

Recent work has proposed the use of a composite hypothesis Hoeffding test for statistical anomaly detection. Setting an appropriate threshold for the test given a desired false alarm probability involves approximating the false alarm…

We present a new approach, inspired by Stein's method, to prove a central limit theorem (CLT) for linear statistics of $\beta$-ensembles in the one-cut regime. Compared with the previous proofs, our result requires less regularity on the…

We prove two theorems related to the Central Limit Theorem (CLT) for Martin-L\"of Random (MLR) sequences. Martin-L\"of randomness attempts to capture what it means for a sequence of bits to be "truly random". By contrast, CLTs do not make…

The purpose of this paper is to provide a first class of explicit sufficient conditions for the central limit theorem and related results in the setup of non-uniformly (partially) expanding non iid random transformations, considered as…

Suppose $B_i:= B(p,r_i)$ are nested balls of radius $r_i$ about a point $p$ in a dynamical system $(T,X,\mu)$. The question of whether $T^i x\in B_i$ infinitely often (i. o.) for $\mu$ a.e.\ $x$ is often called the shrinking target problem.…

In this paper we establish spatial central limit theorems for a large class of supercritical branching Markov processes with general spatial-dependent branching mechanisms. These are generalizations of the spatial central limit theorems…

In this paper we establish a general dynamical Central Limit Theorem (CLT) for group actions which are exponentially mixing of all orders. In particular, the main result applies to Cartan flows on finite-volume quotients of simple Lie…

The \textit{Central Limit Theorem (CLT)} is at the heart of a great deal of applied problem-solving in statistics and data science, but the theorem is silent on an important implementation issue: \textit{how much data do you need for the…

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain…

This paper is concerned with the limiting spectral behaviors of large dimensional Kendall's rank correlation matrices generated by samples with independent and continuous components. We do not require the components to be identically…

We consider deterministic random walks on the real line driven by irrational rotations, or equivalently, skew product extensions of a rotation by $\alpha$ where the skewing cocycle is a piecewise constant mean zero function with a jump by…

Let $Q$ be a transition probability on a measurable space $E$, let $(X\_n)\_n$ be a Markov chain associated to $Q$, and let $\xi$ be a real-valued measurable function on $E$, and $S\_n = \sum\_{k=1}^{n} \xi(X\_k)$. Under functional…

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 obtain convergence rates (in the Levi-Prokhorove metric) in the functional central limit theorem (CLT) for partial sums $S_n=\sum_{j=1}^{n}\xi_{j,n}$ of triangular arrays $\{\xi_{1,n},\xi_{2,n},...,\xi_{n,n}\}$ satisfying some mixing and…

Let $(\tau_n)$ be a sequence of toral automorphisms $\tau_n : x \rightarrow A_n x \hbox{mod}\ZZ^d$ with $A_n \in {\cal A}$, where ${\cal A}$ is a finite set of matrices in $SL(d, \mathbb{Z})$. Under some conditions the method of…