Upper-lower class tests for weighted i.i.d. sequences and martingales

DOI10.1007/s10959-009-0219-5zbMath1200.60025OpenAlexW2006209884MaRDI QIDQ975330

István Berkes, Michel J. G. Weber, Siegfried Hörmann

Publication date: 9 June 2010

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

Full work available at URL: https://doi.org/10.1007/s10959-009-0219-5

zbMATH Keywords

law of the iterated logarithmmartingale difference sequencesweighted sums of i.i.d. random variablesupper-lower class test

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Related Items (1)

Feller’s upper-lower class test in Euclidean space

Cites Work

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• Invariance principles for martingales and sums of independent random variables
• A theorem of Feller revisited
• A Skorohod representation and an invariance principle for sums of weighted i.i.d. random variables
• Upper and lower functions for martingales and mixing processes
• The Darling-Erdős theorem for sums of i.i.d. random variables
• Convergence of the \(p\)-series for stationary sequences
• Darling-Erdős theorems for martingales
• Invariance principles for the law of the iterated logarithm for martingales and processes with stationary increments
• The law of the iterated logarithm for identically distributed random variables
• A law of the iterated logarithm for arithmetic functions
• Weighted ergodic theorems and strong laws of large numbers
• Convergence of weighted averages of independent random variables
• The General Form of the So-Called Law of the Iterated Logarithm

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