Weak laws of large numbers for weighted independent random variables with infinite mean

DOI10.1016/j.spl.2015.11.017zbMath1329.60040OpenAlexW2177869990MaRDI QIDQ899647

Toshio Nakata

Publication date: 30 December 2015

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2015.11.017

zbMATH Keywords

regular variationweak laws of large numbersinfinite meanPareto-Zipf distributionsweighted independent random variables

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05)

Related Items (18)

Some limit theorems for weighted negative quadrant dependent random variables with infinite mean ⋮ One sided strong laws for random variables with infinite mean ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Weak laws of large numbers for nonnegative independent random variables without finite means ⋮ Unnamed Item ⋮ Limit theorems for dependent random variables with infinite means ⋮ Marcinkiewicz–Zygmund type strong law of large numbers for weighted sums of random variables with infinite moment and its applications ⋮ Exact weak laws of large numbers with applications to ratios of random variables ⋮ Weak and one-sided strong laws for random variables with infinite mean ⋮ Exact laws of large numbers for independent Pareto random variables ⋮ Unnamed Item ⋮ Large deviations for super-heavy tailed random walks ⋮ On exact laws of large numbers for Oppenheim expansions with infinite mean ⋮ Laws of large numbers with infinite mean ⋮ Convergence in mean and central limit theorems for weighted sums of martingale difference random vectors with infinite rth moments ⋮ Weighted Laws of Large Numbers for a class of independent summands ⋮ The laws of large numbers for Pareto-type random variables with infinite means

Cites Work

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• An extension of the Kolmogorov-Feller weak law of large numbers with an application to the St. Petersburg game
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• On the nonexistence of a law of the iterated logarithm for weighted sums of identically distributed random variables
• Limit theorems for nonnegative independent random variables with truncation
• Laws of large numbers for asymmetrical Cauchy random variables
• Relative stability and the strong law of large numbers
• Limit Theorems for a Generalized Feller Game
• Probability: A Graduate Course

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