COMPLETE CONVERGENCE FOR ARRAYS AND THE LAW OF THE SINGLE LOGARITHM

DOI10.1017/S0004972717000582zbMath1374.60047MaRDI QIDQ5369411

Ulrich Stadtmüller, Allan Gut

Publication date: 17 October 2017

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

complete convergenceexponential boundsarraysindependent and identically distributedBorel-Cantelli lemmasthe law of the iterated logarithmrow-wise independencethe strong law of large numbers

Mathematics Subject Classification ID

Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15)

Cites Work

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• Kolmogorov type law of the logarithm for arrays
• Strong laws for sequences in the vicinity of the LIL
• A note on the law of iterated logarithm for weighted sums of random variables
• The weak law of large numbers for arrays
• Complete convergence for arrays
• Almost sure limit behaviour of Cesàro sums with small order
• Variants on the Law of the Iterated Logarithm
• On strong convergence of arrays
• An analogue of Kolmogorov's law of the iterated logarithm for arrays
• A converse to the law of the iterated logarithm
• On the Law of the Iterated Logarithm
• Complete Convergence and the Law of Large Numbers
• On a Theorem of Hsu and Robbins
• Remark on my Paper "On a Theorem of Hsu and Robbins"
• Probability: A Graduate Course

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