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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Weak laws for dependent sums

Author: William L. Steiger
Journal: Proc. Amer. Math. Soc. 41 (1973), 278-281
MSC: Primary 60F05
MathSciNet review: 0319242
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Abstract: A general weak law of large numbers for sums $ {S_n} = {X_1} + \cdots + {X_n}$ is proved. That is, without assuming the existence of any moments, and allowing any sort of dependence structure, conditions are given for $ {S_n}/n \to 0$ in probability; the conditions are not necessary. However they are sufficient for a much stronger statement, namely that $ {S_{{\nu _n}}}/{\nu _n} \to 0$ in probability in many cases where positive, integer-valued random variables $ {\nu _n} \to \infty $.

References [Enhancements On Off] (What's this?)

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  • [4] Pál Révész, The laws of large numbers, Probability and Mathematical Statistics, Vol. 4, Academic Press, New York-London, 1968. MR 0245079

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Keywords: Weak law of large numbers, dependent random variables, random sums
Article copyright: © Copyright 1973 American Mathematical Society