## The Annals of Probability

- Ann. Probab.
- Volume 14, Number 3 (1986), 1088-1094.

### A Note on Feller's Strong Law of Large Numbers

Yuan Shih Chow and Cun-Hui Zhang

#### Abstract

Let $X_n, n \geq 1$, be i..d. random variables with common distribution function $F(x)$ and $\gamma_n, n \geq 1$, be a sequence of constants such that $\gamma_n/n$ is nondecreasing in $n$. Set $S_n = X_1 + \cdots + X_n$. The main theorem of this paper gives an integral test which determines the infinite limit points of $\{S_n/\gamma_n\}$. This result extends and combines Feller's (1946) strong law of large numbers (SLLN) and the results Kesten (1970) and Erickson (1973).

#### Article information

**Source**

Ann. Probab., Volume 14, Number 3 (1986), 1088-1094.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aop/1176992464

**Digital Object Identifier**

doi:10.1214/aop/1176992464

**Mathematical Reviews number (MathSciNet)**

MR841610

**Zentralblatt MATH identifier**

0608.60052

**JSTOR**

links.jstor.org

**Subjects**

Primary: 60G50: Sums of independent random variables; random walks

Secondary: 60J15 60F16 60F20: Zero-one laws

**Keywords**

Normed sums of independent random variables integral tests

#### Citation

Chow, Yuan Shih; Zhang, Cun-Hui. A Note on Feller's Strong Law of Large Numbers. Ann. Probab. 14 (1986), no. 3, 1088--1094. doi:10.1214/aop/1176992464. https://projecteuclid.org/euclid.aop/1176992464