A Note on Feller's Strong Law of Large Numbers
Chow, Yuan Shih ; Zhang, Cun-Hui
Ann. Probab., Tome 14 (1986) no. 4, p. 1088-1094 / Harvested from Project Euclid
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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).
Publié le : 1986-07-14
Classification:  Normed sums of independent random variables,  integral tests,  60G50,  60J15,  60F16,  60F20 
@article{1176992464,
     author = {Chow, Yuan Shih and Zhang, Cun-Hui},
     title = {A Note on Feller's Strong Law of Large Numbers},
     journal = {Ann. Probab.},
     volume = {14},
     number = {4},
     year = {1986},
     pages = { 1088-1094},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176992464}
}

Chow, Yuan Shih; Zhang, Cun-Hui. A Note on Feller's Strong Law of Large Numbers. Ann. Probab., Tome 14 (1986) no. 4, pp.  1088-1094. http://gdmltest.u-ga.fr/item/1176992464/