English
Related papers

Related papers: Central limit theorems for nonlinear hierarchical …

200 papers

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…

Probability · Mathematics 2019-12-11 Li-Xin Zhang

A finite range interacting particle system on a transitive graph is considered. Assuming that the dynamics and the initial measure are invariant, the normalized empirical distribution process converges in distribution to a centered…

Mathematical Physics · Physics 2007-05-23 Paul Doukhan , Gabriel Lang , Sana Louhichi , Bernard Ycart

We prove a central limit theorem for a certain class of functions on sparse rank-one inhomogeneous random graphs endowed with additional i.i.d. edge and vertex weights. Our proof of the central limit theorem uses a perturbative form of…

Probability · Mathematics 2024-04-22 Anja Sturm , Moritz Wemheuer

In this paper, we give the central limit theorem and almost sure central limit theorem for products of some partial sums of independent identically distributed random variables.

Probability · Mathematics 2007-08-01 Yu Miao

We develop a central limit theorem (CLT) for a non-parametric estimator of the transition matrices in controlled Markov chains (CMCs) with finite state-action spaces. Our results establish precise conditions on the logging policy under…

Statistics Theory · Mathematics 2026-03-26 Ziwei Su , Imon Banerjee , Diego Klabjan

Recently a new type of central limit theorem for belief functions was given in Epstein et al. [9]. In this paper, we generalize the central limit theorem in Epstein et al. [9] to accommodate general bounded random variables. These results…

Probability · Mathematics 2017-12-21 Xiaomin Shi

We consider a class of random billiards in a tube, where reflection angles at collisions with the boundary of the tube are random variables rather than deterministic (and elastic) quantities. We obtain a (non-standard) Central Limit Theorem…

Dynamical Systems · Mathematics 2025-07-21 Henk Bruin , Niels Kolenbrander , Dalia Terhesiu

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.

Probability · Mathematics 2026-01-06 S. V. Dzhenzher , V. Zh. Sakbaev

We established the rate of convergence in the central limit theorem for stopped sums of a class of martingale difference sequences.

Probability · Mathematics 2015-06-26 Lahcen Ouchti

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…

Statistics Theory · Mathematics 2018-10-11 Anna Czapkiewicz , Antoni Dawidowicz

We study inhomogeneous random graphs with a finite type space. For a natural generalization of the model as a dynamic network-valued process, the paper establishes the following results: (a) Functional central limit theorems for the…

Probability · Mathematics 2025-01-22 Shankar Bhamidi , Amarjit Budhiraja , Akshay Sakanaveeti

Using an averaged generating function for coloured hard-dimers, some random variables of interest are studied. The main result lies in the fact that all their probability distributions obey a central limit theorem.

Probability · Mathematics 2009-06-22 Maria Simonetta Bernabei , Horst Thaler

We establish central limit theorems for general functionals on binomial point processes and their Poissonized version. As an application, a central limit theorem for Betti numbers of random geometric complexes in the thermodynamic regime is…

Probability · Mathematics 2018-04-10 Khanh Duy Trinh

In this paper, we obtain a new estimate for uniform integrability under sublinear expectations. Based on this, we establish the limit theorems under nonlinear expectations dominated by sublinear expectations through tightness, and the limit…

Probability · Mathematics 2025-06-23 Xiaojuan Li , Mingshang Hu

We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…

Dynamical Systems · Mathematics 2020-01-08 Olli Hella , Mikko Stenlund

We present a central limit theorem for stationary random fields that are short-range dependent and asymptotically independent. As an application, we present a central limit theorem for an infinite family of interacting It\^o-type diffusion…

Probability · Mathematics 2021-10-19 Le Chen , Davar Khoshnevisan , David Nualart , Fei Pu

In this paper, we investigate a central limit theorem for weighted sums of independent random variables under sublinear expectations. It is turned out that our results are natural extensions of the results obtained by Peng and Li and Shi.

Probability · Mathematics 2011-05-05 Defei Zhang

In this paper, we derive asymptotic results for L^1-Wasserstein distance between the distribution function and the corresponding empirical distribution function of a stationary sequence. Next, we give some applications to dynamical systems…

Probability · Mathematics 2008-12-16 Sophie Dede

We consider asymptotic behavior of Fourier transforms of stationary ergodic sequences with finite second moments. We establish a central limit theorem (CLT) for almost all frequencies and also an annealed CLT. The theorems hold for all…

Probability · Mathematics 2010-11-08 Magda Peligrad , Wei Biao Wu

We consider the random walk among random conductances on Z^d. We assume that the conductances are independent, identically distributed and uniformly bounded away from 0 and infinity. We obtain a quantitative version of the central limit…

Probability · Mathematics 2011-05-24 Jean-Christophe Mourrat