On the universal a.s. central limit theorem

DOI10.1007/s10474-007-6070-1zbMath1164.60016OpenAlexW2114331905MaRDI QIDQ950290

Siegfried Hörmann

Publication date: 22 October 2008

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-007-6070-1

zbMATH Keywords

summation methodsalmost sure limit theory

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15)

Related Items (12)

Large deviations for some logarithmic means in the case of random variables with thin tails ⋮ Some distributional limit theorems for the maxima of Gaussian vector sequences ⋮ Almost sure central limit theorem for the hybrid process ⋮ Asymptotic results for weighted means of linear combinations of independent Poisson random variables ⋮ An extension of almost sure central limit theorem for order statistics ⋮ Large deviation principles for sequences of logarithmically weighted means ⋮ Almost sure convergence of extreme order statistics ⋮ Quantitative recurrence results for random walks ⋮ Asymptotic results for weighted means of random variables which converge to a Dickman distribution, and some number theoretical applications ⋮ Large deviations for weighted means of random vectors defined in terms of suitable Lévy processes ⋮ On large deviations for some sequences of weighted means of Gaussian processes ⋮ A Borel-Cantelli lemma and its applications

Cites Work

• On almost sure max-limit theorems
• A note on the almost sure central limit theorem
• Some limit theorems in log density
• A limit theorem for the maximum of normalized sums of independent random variables
• Convex-invariant means and a pathwise central limit theorem
• Extension of the Darling and Erdős theorem on the maximum of normalized sums
• An almost sure central limit theorem for independent random variables
• On the logarithmic average of additive functionals
• On strong versions of the central limit theorem.
• The almost sure central limit theorem
• Almost sure limit theorems for the maximum of stationary Gaussian sequences
• Almost sure versions of distributional limit theorems for certain order statistics.
• A universal result in almost sure central limit theory.
• Weight functions and pathwise local central limit theorems
• Logarithmic averages for the local times of recurrent random walks and Lévy processes
• An almost sure central limit theorem with generalized moments for irrational rotations
• Critical behavior in almost sure central limit theory
• Almost sure versions of the Darling-Erdős theorem
• On Almost Sure Limit Theorems
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
• Almost Sure Convergence in Extreme Value Theory
• The Intersective ASCLT
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the universal a.s. central limit theorem