The Annals of Probability

A Note on Feller's Strong Law of Large Numbers

Yuan Shih Chow and Cun-Hui Zhang

Full-text: Open access

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


Export citation