|
|
| |
| Strong Convergence for Weighted Sums of Negatively Associated Arrays |
| |
Citation： |
Hanying LIANG,Jingjing ZHANG.Strong Convergence for Weighted Sums of Negatively Associated Arrays[J].Chinese Annals of Mathematics B,2010,31(2):273~288 |
| Page view： 1995
Net amount： 1622 |
Authors： |
Hanying LIANG; Jingjing ZHANG; |
Foundation： |
the National Natural Science Foundation of China (No. 10871146), the Spanish
Ministry of Science and Innovation (No. MTM2008-03129), and the Xunta de Galicia, Spain (No.
PGIDIT07PXIB300191PR). |
|
|
| Abstract： |
Let $\{X_{ni}\}$ be an array of rowwise negatively associated random
variables and $T_{nk} = \sum\limits_{i=1}^k i^\a X_{ni}$ for
$\a\>-1,$ $S_{nk} =
\sum\limits_{|i|\\e B_n\Big)<\oo
\quad\mbox{and}\quad
\sum\limits^\oo_{n=1}C_nP\Big(\max\limits_{0\\e D_n\Big)<\oo
$$
for all $\e>0$, where $A_n,B_n,C_n$ and $D_n$ are some positive
constants, $m_n\in \mN$ with $\frac{m_n}{n^\h}\to\oo$. The results
of Lanzinger and Stadtm\"uller in 2003 are extended from the i.i.d.
case to the case of the negatively associated, not necessarily
identically distributed random variables. Also, the result of Pruss
in 2003 on independent variables reduces to a special case of the
present paper; furthermore, the necessity part of his result is
complemented. |
Keywords： |
Tail probability, Negatively associated random variable, Weighted sum |
Classification： |
60F15 |
|
|
Download PDF Full-Text
|
|
|
|
