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|Title:||Hyperfinite law of large numbers|
|Citation:||Sun, Y. (1996-06). Hyperfinite law of large numbers. Bulletin of Symbolic Logic 2 (2) : 189-198. ScholarBank@NUS Repository.|
|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.|
|Source Title:||Bulletin of Symbolic Logic|
|Appears in Collections:||Staff Publications|
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