Commun. Korean Math. Soc. 2003; 18(1): 117-126
Printed March 1, 2003
Copyright © The Korean Mathematical Society.
Jong-Il Baek, Dong-Myong Lee
Wonkwang University, Wonkwang University
Let $\{ X_{n k}~ | 1 \leq k \le n, n \ge 1 \}$ be an array of row negatively associated ($NA$) random variables which satisfy $P(|X_{nk} | >x) \le P(|X|>x)$. For weighed sums $ \sum_{k=1}^{T_n} a_k X_{nk}$ indexed by random variables $\{T_n | n \geq 1 \}$, we establish a general weak law of large numbers ($WLLN$) of the form $ \left( \sum_{k=1}^{T_n} a_k X_{nk} - \nu_{[nk]} \right) / b_{[\alpha_n]}$ under some suitable conditions, where $\{a_n | n \ge 1 \}$, $\{b_n | n \ge 1 \}$ are sequences of constants with $a_n > 0,~ 0
Keywords: negatively associated random variables, weighted sums indexed by random variables, weak law of large numbers, martingale difference sequence
MSC numbers: 60F05
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