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Zbl 1027.60028
Sung, Soo Hak
Strong laws for weighted sums of i. i. d. random variables. II.
(English)
[J] Bull. Korean Math. Soc. 39, No.4, 607-615 (2002). ISSN 1015-8634

[For part I see Stat. Probab. Lett. 52, 413-419 (2001; Zbl 1020.60016).]\par Let $\{X, X_n$,$n\ge 1\}$ be a sequence of i.i.d. random variables and $\{ a_{ni}$, $1\le i\le n$, $n\ge 1\}$ an array of constants. Let $\varphi (x)$ be a positive increasing function on $(0,\infty)$ satisfying $\varphi (x) \uparrow \infty$ and $\varphi (Cx)=O(\varphi (x))$ for any $C>0.$ Let us assume that $EX=0$ and $E[\varphi (|X|)]<\infty.$ The author presents various conditions on $\varphi$ and $a_{ni}$ under which $\sum_{i=1}^n a_{ni}X_i \to 0$ a.s.
[Zdzislaw Rychlik (Lublin)]
MSC 2000:
*60F15 Strong limit theorems
60G50 Sums of independent random variables

Keywords: strong laws of large numbers; weighted sums

Citations: Zbl 1020.60016

Cited in: Zbl 1165.60317

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