On the almost sure central limit theorem and domains of attraction

DOI10.1007/BF01295218zbMath0821.60030OpenAlexW1995171698MaRDI QIDQ1892255

István Berkes

Publication date: 5 July 1995

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01295218

zbMATH Keywords

domain of attractionalmost sure central limit theoremweight sequencesdomain of partial attraction

Mathematics Subject Classification ID

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

Related Items (12)

A universal result in almost sure central limit theory. ⋮ Almost sure versions of limit theorems for random sums of multiindex random variables ⋮ Some distributional limit theorems for the maxima of Gaussian vector sequences ⋮ On the logarithmic average of iterated processes ⋮ On the pointwise central limit theorem and mixtures of stable distributions ⋮ Diophantine equations and the LIL for the discrepancy of sublacunary sequences ⋮ Some optimal conditions for the ASCLT ⋮ On almost sure max-limit theorems ⋮ Almost sure central limit theorems for functionals of absolutely regular processes with application to \(U\)-statistics ⋮ Logarithmic averages of stable random variables are asymptotically normal ⋮ Almost sure limit theorems for random sums of multiindex random variables ⋮ An almost sure limit theorem for random sums of independent random variables in the domain of attraction of a semistable law

Cites Work

• A note on the almost sure central limit theorem
• Some limit theorems in log density
• On the almost sure (a.s.) central limit theorem for random variables with infinite variance
• On Strong Versions of the Central Limit Theorem
• An almost everywhere central limit theorem
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