Related papers: A weighted central limit theorem under sublinear e…
This paper provides central limit theorems for the wavelet packet decomposition of stationary band-limited random processes. The asymptotic analysis is performed for the sequences of the wavelet packet coefficients returned at the nodes of…
The Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of $n$ mutually independent and identically distributed random variables with finite first and…
In this work, we develop a numerical method to study the error estimates of the $\alpha$-stable central limit theorem under sublinear expectation with $\alpha \in(0,2)$, whose limit distribution can be characterized by a fully nonlinear…
We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are straightforward extensions of the univariate case.
Short and transparent proofs of central limit theorems for intrinsic volumes of random polytopes in smooth convex bodies are presented. They combine different tools such as estimates for floating bodies with Stein's method from probability…
We derive a central limit theorem for the probability distribution of the sum of many critically correlated random variables. The theorem characterizes a variety of different processes sharing the same asymptotic form of anomalous scaling…
We give a new, self-contained proof of the multidimensional central limit theorem using the technique of ``doubling variables," which is traditionally used to prove uniqueness of solutions of partial differential equations (PDEs). Our…
We prove a central limit theorem for the volume of projections of the N-cube onto a random subspace of dimension n, when n is fixed and N tends to infinity. Randomness in this case is with respect to the Haar measure on the Grassmannian…
Classical Kolmogorov's and Rosenthal's inequalities for the maximum partial sums of random variables are basic tools for studying the strong laws of large numbers. In this paper, motived by the notion of independent and identically…
The Central Limit Theorem (CLT) establishes that sufficiently large sequences of independent and identically distributed random variables converge in probability to a normal distribution. This makes the CLT a fundamental building block of…
Consider a sequence of $n$ independent random variables with a common continuous distribution $F$, and consider the task of choosing an increasing subsequence where the observations are revealed sequentially and where an observation must be…
The law of large numbers for the empirical density for the pairs of uniformly distributed integers with a given greatest common divisor is a classic result in number theory. In this paper, we study the large deviations of the empirical…
Let $G$ be an $N \times N$ real matrix whose entries are independent identically distributed standard normal random variables $G_{ij} \sim \mathcal{N}(0,1)$. The eigenvalues of such matrices are known to form a two-component system…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
A sharp version of the Central Limit Theorem for linear combinations of iterates of an inner function is proved. The authors previously showed this result assuming a suboptimal condition on the coefficients of the linear combination. Here…
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…
In this paper we survey and further study partial sums of a stationary process via approximation with a martingale with stationary differences. Such an approximation is useful for transferring from the martingale to the original process the…
The goal of this paper is to describe conditions which guarantee a central limit theorem for random variables, which distributions are controled by hidden Markov chains. We proved that when a Markov chain is ergodic and random variables…
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…
The "typical" asymptotic behavior of the weighted sums of independent, identically distibuted random vectors in k-dimensional space is considered. It is shown that under finitnes of fifth absolute moment of an individual term the rate of…