Related papers: The Central Limit Theorem for function systems on …

Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.

We study the infinite urn scheme when the balls are sequentially distributed over an infinite number of urns labelled 1,2,... so that the urn $j$ at every draw gets a ball with probability $p_j$, $\sum_j p_j=1$. We prove functional central…

A discrete quantum process is represented by a sequence of quantum operations, which are completely positive maps that are not necessarily trace preserving. We consider quantum processes that are obtained by repeated iterations of a quantum…

In this paper a generalized topological central point theorem is proved for maps of a simplex to finite-dimensional metric spaces. Similar generalizations of the Tverberg theorem are considered.

We consider a multidimensional random walk in a product random environment with bounded steps, transience in some spatial direction, and high enough moments on the regeneration time. We prove an invariance principle, or functional central…

We prove results about uniform convergence of densities in the free central limit theorem without assumptions of boundedness on the support.

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…

This paper provides refined versions of some known functional central limit theorems for conditional Poisson sampling which are more suitable for applications. The theorems presented in this paper are generalizations of some results that…

We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for different k.

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 investigate a sequence of square integrable random processes with space varying memory. We establish sufficient conditions for the central limit theorem in the space $L^2(\mu)$ for the partial sums of the sequence of random…

We prove a functional central limit theorem for partial sums of symmetric stationary long range dependent heavy tailed infinitely divisible processes with a certain type of negative dependence. Previously only positive dependence could be…

We prove a functional limit theorem in a space of analytic functions for the random Dirichlet series $D(\alpha;z)=\sum_{n\geq 2}(\log n)^{\alpha}(\eta_n+{\rm i} \theta_n)/n^z$, properly scaled and normalized, where…

We find an asymptotic expansion of a multi-dimensional version of Selberg's central limit theorem for $L$-functions on $ \sigma= \frac12 + ( \log T)^{-\theta}$ and $ t \in [ T, 2T]$, where $ 0 < \theta < \frac12 $ is a constant.

We consider a positive recurrent one-dimensional diffusion process with continuous coefficients and we establish stable central limit theorems for a certain type of additive functionals of this diffusion. In other words we find some…

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…

In this paper we study the central limit theorem for additive functionals of stationary Markov chains with general state space by using a new idea involving conditioning with respect to both the past and future of the chain. Practically, we…

We check claims for a generalized central limit theorem holding at the Feigenbaum (infinite bifurcation) point of the logistic map, made recently by U. Tirnakli, C. Beck, and C. Tsallis (Phys. Rev. {\bf 75}, 040106(R) (2007)). We show that…

We study the dynamics of iteration function systems generated by a pair of circle diffeomorphisms close to rotations in the $C^{1+\mathrm{bv}}$-topology. We characterize the obstruction to minimality and describe the limit set. In…

For a $d\times d$ expanding matrix $A$, we investigate randomness of the sequence $\{A^k x\}$ and prove the central limit theorem for $\sum f(A^k x)$ where $f$ is a periodic function with a mild regularity condition.