Almost sure convergence for weighted sums of I.I.D. random variables (II)

摘要

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 $limsup_{no infty}sum_{i=1}^na_{ni}X_ile 1$ a.s. when $EX_1^2=1$ and $max_{1le ile n}|a_{ni}|le 1/sqrt{2nlog n}.$