Bulletin of the
Korean Mathematical Society BKMS

This paper is concerned with the almost sure convergence for weighted sums $\sum_{i=1}^na_{ni}X_i$ of i.i.d. random variables with mean zero and finite second moment. It is shown that $\limsup_{n\to \infty}\sum_{i=1}^na_{ni}X_i\le 1$ a.s. when $EX_1^2=1$ and $\max_{1\le i\le n}|a_{ni}|\le 1/\sqrt{2n\log n}.$

Keywords: almost sure convergence, weighted sums, triangular arrays

MSC numbers: 60F15