Some examples of application of the metric entropy method
type: Item
instance of: scholarly article
title: Some examples of application of the metric entropy method
zbMATH Open document ID: 1068.60056
published in: Acta Mathematica Hungarica
publication date: 2005-07-05T00:00:00Z
review text: Using the metric entropy method, the author gives a common proof to various important tools used in establishing almost sure convergence of sequences of functions, evaluating suprema and counting up the number of occurrences of events. The author describes a unified setting suitable to prove a number of classical results, like the Rademacher-Menshov theorem, the Stechkin theorem, the Gál-Koksma theorems, the quantitative versions of Borel-Cantelli lemma. The examples concern upper and lower classes for stationary Gaussian sequences and the law of the iterated logarithm for subsequences and the Diophantine approximation relatively to Gál and Schmidt's theorems.
Mathematics Subject Classification ID: 60G17
Mathematics Subject Classification ID: 42C15
Mathematics Subject Classification ID: 11J83
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 60F15
zbMATH DE Number: 2186357
zbMATH Keywords: dyadic chaining
zbMATH Keywords: almost sure convergence
zbMATH Keywords: quantitative Borel-Cantelli Lemma
zbMATH Keywords: Stechkin theorem
zbMATH Keywords: Gál-Koksma theorem
zbMATH Keywords: Diophantine approximation
zbMATH Keywords: law of the iterated logarithm
zbMATH Keywords: subsequences
zbMATH Keywords: upper classes
zbMATH Keywords: lower classes
zbMATH Keywords: stationary Gaussian sequences
author: Michel Weber
MaRDI profile type: Publication
cites work: Q3278441
cites work: Metric Number Theory and the Large Sieve
cites work: Q4137830
cites work: Q5560061
cites work: Q5619860
cites work: Q5544740
cites work: Borel—Cantelli type theorems for mixing sets
cites work: Functional central limit theorem and Strassen's law of the iterated logarithms for weakly multiplicative systems
cites work: LACUNARY SERIES AND INDEPENDENT FUNCTIONS
cites work: Q5580762
cites work: Q5787957
cites work: Q5800881
cites work: Note on a Property of Measurable Sets
cites work: Q4389330
cites work: Q3856819
cites work: THE FUNCTIONAL LAW OF THE ITERATED LOGARITHM FOR WEAKLY MULTIPLICATIVE SYSTEMS
cites work: Decoupling inequalities for stationary Gaussian processes
cites work: Q5793895
cites work: Q3993061
cites work: A Gap Theorem
cites work: Remark on a Paper of Visser
cites work: Spectral regularization inequalities
cites work: Analytic Inequalities
cites work: The law of the iterated logarithm and related results for weakly multiplicative systems
cites work: Q3909753
cites work: Moment and probability bounds with quasi-superadditive structure for the maximum partial sum
cites work: Une d�monstration �l�mentaire du th�or�me de r�currence
cites work: Q4085018
cites work: Some metrical theorems in number theory
cites work: Some metrical theorems in number theory. II. - Errata
cites work: Q3883230
cites work: On mixing sequences of sets
cites work: A law of the iterated logarithm for weakly multiplicative systems and its applications
cites work: The size of the averages of strongly mixing random variables
cites work: On the subspaces of \(L^p\) \((p > 2)\) spanned by sequences of independent random variables
cites work: Metrical Theorems on Fractional Parts of Sequences
cites work: Q3939894
cites work: An invariance principle for the law of the iterated logarithm
cites work: Note on mixing sequences of events
cites work: Sample boundedness of stochastic processes under increment conditions
cites work: Q5803461
cites work: Q5766479
cites work: The law of the iterated logarithm on subsequences-characterizations
cites work: Q4223601
cites work: Controlling orthogonal series with irrational rotations
cites work: Estimating random polynomials by means of metric entropy methods
cites work: Some theorems related to almost sure convergence of orthogonal series
cites work: Discrepancy of randomly sampled sequences of reals
cites work: An arithmetical property of Rademacher sums.
cites work: Uniform bounds under increment conditions
DOI: 10.1023/B:AMHU.0000045531.17229.D4
Recommended article: Metric Entropy estimation using o-minimality Theory
Recommended article: Metric entropy of some classes of sets

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Selection of a metric for the nearest neighbor entropy estimators
Similarity Score: 0.83879375
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Q4416555
Similarity Score: 0.830244
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Metric entropy of high dimensional distributions
Similarity Score: 0.82870674
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Q3651822
Similarity Score: 0.8283426
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: On entropy estimation by \(m\)-spacing method
Similarity Score: 0.82699484
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Q4441314
Similarity Score: 0.82665896
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Relative entropy method for measure-valued solutions in natural sciences
Similarity Score: 0.82606715
Recommender Run: Recommender Run 3

Some examples of application of the metric entropy method (Recommended article)
Recommended article: Q5420949
Similarity Score: 0.82504684
Recommender Run: Recommender Run 3