Critical behavior in almost sure central limit theory

DOI10.1007/S10959-007-0080-3zbMath1132.60029OpenAlexW2132032896MaRDI QIDQ2385613

Siegfried Hörmann

Publication date: 12 October 2007

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-007-0080-3

zbMATH Keywords

law of the iterated logarithmalmost sure central limit theoremsummation methods

Mathematics Subject Classification ID

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

Related Items (18)

An improved result in almost sure local central limit theorem for the partial sums ⋮ An improved result in almost sure central limit theorem for self-normalized products of partial sums ⋮ Almost sure central limit theorem for self-normalized partial sums and maxima ⋮ Some distributional limit theorems for the maxima of Gaussian vector sequences ⋮ Almost sure convergence for self-normalized products of sums of partial sums of ρ¯-mixing sequences ⋮ A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law ⋮ Almost sure central limit theory for products of sums of partial sums ⋮ Almost sure central limit theorem for self-normalized partial sums of \(\rho^{-}\)-mixing sequences ⋮ Some optimal conditions for the ASCLT ⋮ Almost sure convergence of extreme order statistics ⋮ Almost sure central limit theory for self-normalized products of sums of partial sums ⋮ Almost sure central limit theorem for self-normalized products of partial sums of negatively associated sequences ⋮ On the universal a.s. central limit theorem ⋮ Almost sure limit theorems for stable distributions ⋮ An extension of almost sure central limit theorem for the maximum of stationary Gaussian random fields ⋮ Almost sure local central limit theorem for the product of some partial sums of negatively associated sequences ⋮ Improved results in almost sure central limit theorems for the maxima and partial sums for Gaussian sequences ⋮ Almost sure central limit theorem for self-normalized partial sums of negatively associated random variables

Cites Work

• A note on the almost sure central limit theorem
• An improvement of Strassen's invariance principle
• The almost sure central limit theorem
• A universal result in almost sure central limit theory.
• An almost sure central limit theorem with generalized moments for irrational rotations
• Almost sure limit theorems of mantissa type for semistable domains of attraction
• An extension of almost sure central limit theory
• On the law of the iterated logarithm for lacunary trigonometric series
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
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