Journal of the
Korean Mathematical Society JKMS

Let $\{V_{nk}, k \ge 1, n\ge 1\}$ be an array of rowwise independent random elements which are stochastically dominated by a random variable $X$ with $E|X|^{\frac{\alpha}{\gamma}+\theta}\log^\rho (|X|) <\infty$ for some $\rho>0, \alpha>0, \gamma>0, \theta>0$ such that $\theta+\alpha/\gamma<2$. Let $\{a_{nk}, k \ge 1, n\ge 1\}$ be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form $\sum_{k=1}^\infty a_{nk}V_{nk}$.

Keywords: arrays of random elements, rowwise independence, weighted sums, complete convergence, rate of convergence, convergence in probability

MSC numbers: Primary 60B12, 60F05, 60F15