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

MATHEMATICS / Probability & Statistics / General | Central limit theorem

Book

1989, Mathematics and its applications. Soviet series, ISBN 9027728259, xv, 156 p. --

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

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

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

Probability Theory and Related Fields, ISSN 0178-8051, 8/2014, Volume 159, Issue 3, pp. 435 - 478

...Probab. Theory Relat. Fields (2014) 159:435–478 DOI 10.1007/s00440-013-0510-3 Berry–Esseen bounds in the entropic central limit theorem Sergey G. Bobkov...

Berry–Esseen bounds | Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | Berry-Esseen bounds | TRANSPORTATION COST | INEQUALITIES | INFORMATION | STATISTICS & PROBABILITY | Studies | Theorems | Law | Random variables | Probability theory | Sums

Berry–Esseen bounds | Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | Berry-Esseen bounds | TRANSPORTATION COST | INEQUALITIES | INFORMATION | STATISTICS & PROBABILITY | Studies | Theorems | Law | Random variables | Probability theory | Sums

Journal Article

The Annals of probability, ISSN 0091-1798, 2016, Volume 44, Issue 2, pp. 1308 - 1340

We prove a central limit theorem for random walks with finite variance on linear groups.

Central limit theorem | Mathematical theorems | Covariance | Random walk | Law of large numbers | Mathematical moments | Matrices | Random variables | Martingales | Continuous functions | Stationary measure | Cocycle | Semisimple group | Martingale | LARGE NUMBERS | LAW | stationary measure | cocycle | MARKOV-CHAINS | STATIONARY MEASURES | PROJECTIVE SPACES | STATISTICS & PROBABILITY | RANDOM MATRICES | TORUS | RANDOM-WALKS | PRODUCTS | martingale | CONVERGENCE | semisimple group | 60G42 | 60G50 | 22E40

Central limit theorem | Mathematical theorems | Covariance | Random walk | Law of large numbers | Mathematical moments | Matrices | Random variables | Martingales | Continuous functions | Stationary measure | Cocycle | Semisimple group | Martingale | LARGE NUMBERS | LAW | stationary measure | cocycle | MARKOV-CHAINS | STATIONARY MEASURES | PROJECTIVE SPACES | STATISTICS & PROBABILITY | RANDOM MATRICES | TORUS | RANDOM-WALKS | PRODUCTS | martingale | CONVERGENCE | semisimple group | 60G42 | 60G50 | 22E40

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

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

For alpha is an element of (1, 2), we present a generalized central limit theorem for alpha-stable random variables under sublinear expectation...

Sublinear expectation | Partial-integro differential equations | Generalized central limit theorem | Stable distribution | G-BROWNIAN MOTION | generalized central limit theorem | REGULARITY | FRAMEWORK | STATISTICS & PROBABILITY | INTEGRODIFFERENTIAL EQUATIONS | stable distribution | sublinear expectation | REPRESENTATION THEOREM | FORMULA | partial-integro differential equations

Sublinear expectation | Partial-integro differential equations | Generalized central limit theorem | Stable distribution | G-BROWNIAN MOTION | generalized central limit theorem | REGULARITY | FRAMEWORK | STATISTICS & PROBABILITY | INTEGRODIFFERENTIAL EQUATIONS | stable distribution | sublinear expectation | REPRESENTATION THEOREM | FORMULA | partial-integro differential equations

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 2/2018, Volume 170, Issue 1, pp. 229 - 262

... Central limit theorem · Transport distances · Edgeworth expansions · Coupling Mathematics Subject Classi cation 60F 1 Introduction Let F p denote the collection...

Edgeworth expansions | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | Transport distances | Coupling | 60F | Quantitative Finance | CONSTANTS | MINIMAL DISTANCES | STATISTICS & PROBABILITY | Transport | Independent variables | Random variables

Edgeworth expansions | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Probability Theory and Stochastic Processes | Mathematics | Transport distances | Coupling | 60F | Quantitative Finance | CONSTANTS | MINIMAL DISTANCES | STATISTICS & PROBABILITY | Transport | Independent variables | Random variables

Journal Article

PloS one, ISSN 1932-6203, 2015, Volume 10, Issue 12, p. e0145604

... Institute for Physics of Complex Systems, Dresden, Germany, Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany Introduction The Central Limit...

FRACTIONAL DYNAMICS | STOCHASTIC-PROCESS | EDGE TURBULENCE | LEVY FLIGHT | FLUCTUATIONS | MULTIDISCIPLINARY SCIENCES | CONVERGENCE | STABLE LAWS | SCALING LAWS | STATISTICAL-ANALYSIS | POWER-LAW | Models, Theoretical | Probability | Algorithms | Humans | Normal Distribution | Practice | Climatic changes | Central limit theorem | Health aspects | Swimmers | Analysis | Plasma | Data analysis | Normal distribution | Light | Gaussian distribution | Mathematics | Random variables | Stochastic models | Charged particles | Physics

FRACTIONAL DYNAMICS | STOCHASTIC-PROCESS | EDGE TURBULENCE | LEVY FLIGHT | FLUCTUATIONS | MULTIDISCIPLINARY SCIENCES | CONVERGENCE | STABLE LAWS | SCALING LAWS | STATISTICAL-ANALYSIS | POWER-LAW | Models, Theoretical | Probability | Algorithms | Humans | Normal Distribution | Practice | Climatic changes | Central limit theorem | Health aspects | Swimmers | Analysis | Plasma | Data analysis | Normal distribution | Light | Gaussian distribution | Mathematics | Random variables | Stochastic models | Charged particles | Physics

Journal Article

Queueing systems, ISSN 1572-9443, 2018, Volume 91, Issue 1-2, pp. 15 - 47

We establish a central-limit-theorem (CLT) version of the periodic Little’s law (PLL) in discrete time, which complements the sample-path and stationary...

60F25 | Systems Theory, Control | Periodic queues | Probability Theory and Stochastic Processes | L = \lambda W$$ L = λ W | 90B22 | Emergency departments | Business and Management | Central limit theorem | Operations Research/Decision Theory | Little’s law | Weak convergence in $$(\ell _1)^d$$ ( ℓ 1 ) d | Supply Chain Management | 60K25 | Computer Communication Networks | 60F05 | L= λW | Weak convergence in (l | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Weak convergence in (l1)(d) | L =lambda W | Little's law | Laws, regulations and rules | Analysis | Management science | Emergency services | Data analysis | Theorems | Emergency medical services

60F25 | Systems Theory, Control | Periodic queues | Probability Theory and Stochastic Processes | L = \lambda W$$ L = λ W | 90B22 | Emergency departments | Business and Management | Central limit theorem | Operations Research/Decision Theory | Little’s law | Weak convergence in $$(\ell _1)^d$$ ( ℓ 1 ) d | Supply Chain Management | 60K25 | Computer Communication Networks | 60F05 | L= λW | Weak convergence in (l | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Weak convergence in (l1)(d) | L =lambda W | Little's law | Laws, regulations and rules | Analysis | Management science | Emergency services | Data analysis | Theorems | Emergency medical services

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

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

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

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

Edgeworth expansions | Central limit theorem | Diophantine approximation | Probability Theory and Stochastic Processes | Mathematics | Statistics, general | 60F | STATISTICS & PROBABILITY

Journal Article

The Annals of probability, ISSN 0091-1798, 11/2013, Volume 41, Issue 6, pp. 3879 - 3909

.... Central limit theorems for U-statistics of Poisson point processes are shown, with explicit bounds for the Wasserstein distance to a Gaussian random variable...

Central limit theorem | Mathematical theorems | Chaos theory | Mathematical integrals | Hyperplanes | Mathematical inequalities | Calculus | Random variables | Statistics | Perceptron convergence procedure | U-statistic | Wiener-Itô chaos expansion | Poisson point process | Malliavin calculus | Stein'smethod | GAUSSIAN FLUCTUATIONS | Wiener-Ito chaos expansion | STATISTICS & PROBABILITY | GEOMETRIC RANDOM GRAPHS | SPACE | CHAOS | WIENER | PROBABILITY | Stein's method | PLANE | CUMULANTS | FUNCTIONALS | Mathematics - Probability | 60D05 | Stein’s method | 60G55 | Wiener–Itô chaos expansion | 60H07 | 60F05

Central limit theorem | Mathematical theorems | Chaos theory | Mathematical integrals | Hyperplanes | Mathematical inequalities | Calculus | Random variables | Statistics | Perceptron convergence procedure | U-statistic | Wiener-Itô chaos expansion | Poisson point process | Malliavin calculus | Stein'smethod | GAUSSIAN FLUCTUATIONS | Wiener-Ito chaos expansion | STATISTICS & PROBABILITY | GEOMETRIC RANDOM GRAPHS | SPACE | CHAOS | WIENER | PROBABILITY | Stein's method | PLANE | CUMULANTS | FUNCTIONALS | Mathematics - Probability | 60D05 | Stein’s method | 60G55 | Wiener–Itô chaos expansion | 60H07 | 60F05

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

Central limit theorem | Hyperbolic length | Word metric | Surface groups | MATHEMATICS | LENGTH SPECTRUM

Journal Article

Probability Theory and Related Fields, ISSN 0178-8051, 6/2014, Volume 159, Issue 1, pp. 1 - 59

.... random variables, satisfying moment conditions. The validity of the central limit theorem is studied via properties of the Fisher information along convolutions.

Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Edgeworth-type expansions | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | STATISTICS & PROBABILITY | INEQUALITIES | Studies | Probability | Mathematical analysis | Theorems | Convolution | Random variables | Normal distribution | Probability theory | Sums

Entropic distance | Central limit theorem | Mathematical and Computational Biology | Statistics for Business/Economics/Mathematical Finance/Insurance | Theoretical, Mathematical and Computational Physics | Operations Research/Decision Theory | Primary 60E | Edgeworth-type expansions | Probability Theory and Stochastic Processes | Mathematics | Entropy | Quantitative Finance | STATISTICS & PROBABILITY | INEQUALITIES | Studies | Probability | Mathematical analysis | Theorems | Convolution | Random variables | Normal distribution | Probability theory | Sums

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

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

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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