Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

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

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]