Abstract
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 $S_{{n}}/\sqrt{|{n}|h({n})}$.
Citation
Wei-Dong Liu. Zheng-Yan Lin. "Some LIL type results on the partial sums and trimmed sums with multidimensional indices." Electron. Commun. Probab. 12 221 - 233, 2007. https://doi.org/10.1214/ECP.v12-1286
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