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 Electronic Communications in Probability > Vol. 12 (2007) > Paper 22 open journal systems 


Some LIL type results on the partial sums and trimmed sums with multidimensional indices

Wei-Dong Liu, Zhejiang University
Zheng-Yan Lin, Zhejiang University


Abstract
Let {X, Xn; n ∈ Nd} be a field of i.i.d. random variables indexed by d-tuples of positive integers and let Sn=∑k≤nXk. We prove some strong limit theorems for Sn. Also, when d≥ 2 and h(n) satisfies some conditions, we show that there are no LIL type results for Sn/√|n|h(n)


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Pages: 221-233

Published on: July 14, 2007


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Electronic Communications in Probability. ISSN: 1083-589X