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Local Central Limit Theorem for Determinantal Point Processes [PDF]
, 2014 We prove a local central limit theorem (LCLT) for the number of points $N(J)$ in a region $J$ in $\mathbb R^d$ specified by a determinantal point process with an Hermitian kernel.
Forrester, Peter J., Lebowitz, Joel L.
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On Estimation of the Remainder Term in New Asymptotic Expansions in the Central Limit Theorem
Computer Sciences & Mathematics Forum, 2023 We offer a new asymptotic expansion with an explicit remainder estimate in the central limit theorem. The results obtained are essentially based on new forms of asymptotic expansions in the central limit theorem.
Vitaly Sobolev, Sergey Ramodanov
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Central limit theorems for sub-linear expectation under the Lindeberg condition
Journal of Inequalities and Applications, 2018 In this paper, we investigate the central limit theorems for sub-linear expectation for a sequence of independent random variables without assumption of identical distribution. We first give a bound on the distance between the normalized sum distribution
Cheng Hu
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Berry-Esseen theorem and local limit theorem for non uniformly expanding maps [PDF]
, 2004 We prove that, in Young towers with sufficiently small tails, the speed in the central limit theorem is O(1/\sqrt{n}), and the local limit theorem holds.
Gouezel, Sebastien
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Central Limit Theorem for Coloured Hard Dimers
Journal of Probability and Statistics, 2010 We study the central limit theorem for a class of coloured graphs. This means that we investigate the limit behavior of certain random variables whose values are combinatorial parameters associated to these graphs.
Maria Simonetta Bernabei, Horst Thaler
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Central and Local Limit Theorems for Numbers of the Tribonacci Triangle
Mathematics, 2021 In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of ...
Igoris Belovas
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A functional combinatorial central limit theorem [PDF]
, 2009 The paper establishes a functional version of the Hoeffding combinatorial central limit theorem. First, a pre-limiting Gaussian process approximation is defined, and is shown to be at a distance of the order of the Lyapounov ratio from the original ...
Barbour, A. D., Janson, Svante
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Moderate deviations and central limit theorem for positive diffusions
Journal of Inequalities and Applications, 2016 In this paper, we establish a central limit theorem and a moderate deviation principle for the positive diffusions, including the CEV and CIR models. The proof is based on the exponential approximations theorem and Burkholder-Davis-Gundy’s inequality.
Yumeng Li, Shuguang Zhang
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Central limit theorem and Diophantine approximations [PDF]
, 1910 Let $F_n$ denote the distribution function of the normalized sum $Z_n = (X_1 + \dots + X_n)/\sigma\sqrt{n}$ of i.i.d. random variables with finite fourth absolute moment.
Bobkov, Sergey G.
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Moment bounds and central limit theorems for Gaussian subordinated arrays
, 2012 A general moment bound for sums of products of Gaussian vector's functions extending the moment bound in Taqqu (1977, Lemma 4.5) is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non ...
Bardet, Jean-Marc, Surgailis, Donatas
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