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July, 1986 A Note on Feller's Strong Law of Large Numbers
Yuan Shih Chow, Cun-Hui Zhang
Ann. Probab. 14(3): 1088-1094 (July, 1986). DOI: 10.1214/aop/1176992464


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).


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Yuan Shih Chow. Cun-Hui Zhang. "A Note on Feller's Strong Law of Large Numbers." Ann. Probab. 14 (3) 1088 - 1094, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0608.60052
MathSciNet: MR841610
Digital Object Identifier: 10.1214/aop/1176992464

Primary: 60G50
Secondary: 60F16 , 60F20 , 60J15

Keywords: integral tests , Normed sums of independent random variables

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
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