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October, 1973 A Probabilistic Proof of the Normal Convergence Criterion
D. Root, H. Rubin
Ann. Probab. 1(5): 867-869 (October, 1973). DOI: 10.1214/aop/1176996854


By embedding partial sum processes into Brownian motion, it is well known that the deMoivre-Laplace central limit theorem is a consequence of the strong law of large numbers. It is the purpose here to show that the embedding technique can be used to establish both the degenerate convergence criterion and the normal convergence criterion for triangular arrays of uniformly asymptotically negligible random variables.


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D. Root. H. Rubin. "A Probabilistic Proof of the Normal Convergence Criterion." Ann. Probab. 1 (5) 867 - 869, October, 1973.


Published: October, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0271.60030
MathSciNet: MR362455
Digital Object Identifier: 10.1214/aop/1176996854

Primary: 60F05
Secondary: 60G40

Keywords: Brownian motion , Normal convergence , stopping times

Rights: Copyright © 1973 Institute of Mathematical Statistics

Vol.1 • No. 5 • October, 1973
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