The Annals of Probability

A Probabilistic Proof of the Normal Convergence Criterion

D. Root and H. Rubin

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Abstract

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.

Article information

Source
Ann. Probab., Volume 1, Number 5 (1973), 867-869.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176996854

Digital Object Identifier
doi:10.1214/aop/1176996854

Mathematical Reviews number (MathSciNet)
MR362455

Zentralblatt MATH identifier
0271.60030

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Keywords
Brownian Motion stopping times normal convergence

Citation

Root, D.; Rubin, H. A Probabilistic Proof of the Normal Convergence Criterion. Ann. Probab. 1 (1973), no. 5, 867--869. doi:10.1214/aop/1176996854. https://projecteuclid.org/euclid.aop/1176996854


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