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Hyperfinite Law of Large Numbers

Published online by Cambridge University Press:  15 January 2014

Yeneng Sun
Yeneng Sun*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 0511 E-mail: matsuny@math.nus.sg
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Abstract

The Loeb space construction in nonstandard analysis is applied to the theory of processes to reveal basic phenomena which cannot be treated using classical methods. An asymptotic interpretation of results established here shows that for a triangular array (or a sequence) of random variables, asymptotic uncorrelatedness or asymptotic pairwise independence is necessary and sufficient for the validity of appropriate versions of the law of large numbers. Our intrinsic characterization of almost sure pairwise independence leads to the equivalence of various multiplicative properties of random variables.

Type
Research Article
Information
Bulletin of Symbolic Logic , Volume 2 , Issue 2 , June 1996 , pp. 189 - 198
Copyright
Copyright © Association for Symbolic Logic 1986

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References

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