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2014, 2nd edition., Cambridge studies in advanced mathematics, ISBN 0521498848, Volume 142, xii, 472
.... When samples become large, the probability laws of large numbers and central limit theorems are guaranteed to hold uniformly over wide domains... 
MATHEMATICS / Probability & Statistics / General | Central limit theorem
Book
ANNALS OF PROBABILITY, ISSN 0091-1798, 01/2019, Volume 47, Issue 1, pp. 270 - 323
We explore properties of the chi(2) and Renyi distances to the normal law and in particular propose necessary and sufficient conditions under which these distances tend to zero in the central limit theorem... 
central limit theorem | FISHER INFORMATION | Renyi and Tsallis entropies | INEQUALITIES | BOUNDS | chi-divergence | MONOTONICITY | CONVERGENCE | STATISTICS & PROBABILITY | ENTROPY
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 9/2018, Volume 31, Issue 3, pp. 1590 - 1605
We refine the classical Lindeberg–Feller central limit theorem by obtaining asymptotic bounds on the Kolmogorov distance, the Wasserstein distance, and the parameterized Prokhorov distances in terms of a Lindeberg index... 
Stein’s method | Lindeberg–Feller central limit theorem | Kolmogorov metric | Wasserstein metric | Probability Theory and Stochastic Processes | Mathematics | Prokhorov metric | Statistics, general | Lindeberg index | 60F05 | STEINS METHOD | Stein's method | Lindeberg-Feller central limit theorem | STATISTICS & PROBABILITY
Journal Article
Journal Article
Biometrika, ISSN 0006-3444, 6/2013, Volume 100, Issue 2, pp. 519 - 524
Chatterjee et al. (2011) established the consistency of the maximum likelihood estimator in the β-model for undirected random graphs when the number of... 
Miscellanea | Central limit theorem | β-model | Fisher information matrix | DISTRIBUTIONS | beta-model | BIOLOGY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | STATISTICS & PROBABILITY
Journal Article
Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, ISSN 1350-7265, 2016, Volume 22, Issue 4, pp. 2548 - 2578
Journal Article
Probability Theory and Related Fields, ISSN 0178-8051, 2/2018, Volume 170, Issue 1, pp. 229 - 262
Journal Article
PloS one, ISSN 1932-6203, 2015, Volume 10, Issue 12, p. e0145604
Journal Article
Journal of applied probability, ISSN 0021-9002, 09/2013, Volume 50, Issue 3, pp. 760 - 771
.... It has wide applications in neuroscience, finance, and many other fields. In this paper we obtain a functional central limit theorem for the nonlinear Hawkes process... 
Hawkes process | Self-exciting process | Central limit theorem | Point process | Functional central limit theorem | 60G55 | point process | self-exciting process | 60F05 | functional central limit theorem
Journal Article
New Journal of Physics, ISSN 1367-2630, 06/2018, Volume 20, Issue 6, p. 63051
.... More precisely, for a sequence of random variables generated by repeated unsharp quantum measurements, we study the limit distribution of relative frequency... 
quantum information task | quantum measurement | central limit theorem | POVM | quantum random variable | STATES | PHYSICS, MULTIDISCIPLINARY | FINETTI THEOREMS | SYSTEMS | COMMUNICATION | Economic models | Theorems | Entanglement | Random variables | Noise measurement | Quantum phenomena | Convergence
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 1, pp. 385 - 408
The exponential rate of convergence and the Central Limit Theorem for some Markov operators are established... 
Exponential rate of convergence | Central limit theorem | Invariant measures | Markov operators | MATHEMATICS | MATHEMATICS, APPLIED | LAW | CONVERGENCE | ITERATED LOGARITHM | OPERATORS | DIVISION | Markov processes | Analysis
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 12/2018, Volume 31, Issue 4, pp. 2390 - 2411
...J Theor Probab (2018) 31:2390–2411 https://doi.org/10.1007/s10959-017-0770-4 Central Limit Theorem and Diophantine Approximations Sergey G. Bobkov 1 Received... 
Edgeworth expansions | Central limit theorem | Diophantine approximation | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60F | STATISTICS & PROBABILITY
Journal Article
Journal Article
Advances in Mathematics, ISSN 0001-8708, 12/2019, Volume 358, p. 106852
We prove a central limit theorem for the length of closed geodesics in any compact orientable hyperbolic surface... 
Central limit theorem | Hyperbolic length | Word metric | Surface groups | MATHEMATICS | LENGTH SPECTRUM
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 2018, Volume 2018, Issue 1, pp. 1 - 14
..., we get the almost sure central limit theorem for the products of the some partial sums (∏i=1kSk,i(k−1)nμn)μβVk\(({\frac{\prod_{i=1}^{k}S_{k,i}}{(k-1)^{n}\mu ^{n}} )^{\frac{\mu}{\beta V_{k}}} }\), where β>0\(\beta>0... 
Almost sure central limit theorem | Mixing sequence | Products of the some partial sums | Self-normalized | Random variables
Journal Article
Journal of Theoretical Probability, ISSN 0894-9840, 3/2018, Volume 31, Issue 1, pp. 1 - 40
.... In this paper, we prove the corresponding central limit theorem. The limit and the CLT normalization fall into three qualitatively different classes arising from “competition... 
Primary 60F05 | Central limit theorem | Secondary 60G20 | Supercritical branching processes | 60J80 | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | Branching processes | Limit behavior | STATISTICS & PROBABILITY
Journal Article
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