## The Annals of Probability

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

### A Probabilistic Proof of the Normal Convergence Criterion

#### 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