摘要：Let $\{X, X_{{n}}; n\in\mathbb{N}^{d}\}$ be a field of i.i.d. random variables indexed by $d$-tuples of positive integers and let $S_{{n}}=\sum_{{k}\leq{n}}X_{{k}}$. We prove some strong limit theorems for $S_{{n}}$. Also, when $d\geq 2$ and $h({n})$ satisfies some conditions, we show that there are no LIL type results for $S_{{n}}/\sqrt{|{n}|h({n})}$.
关键词：Law of the iterated logarithm; random field; trimmed sums;60F15
