Electronic Communications in Probability

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

Wei-Dong Liu and Zheng-Yan Lin

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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 $S_{{n}}/\sqrt{|{n}|h({n})}$.

Article information

Source
Electron. Commun. Probab., Volume 12 (2007), paper no. 22, 221-233.

Dates
Accepted: 2 July 2007
First available in Project Euclid: 6 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465224965

Digital Object Identifier
doi:10.1214/ECP.v12-1286

Mathematical Reviews number (MathSciNet)
MR2320824

Zentralblatt MATH identifier
1129.60031

Subjects
Primary: 60F15: Strong theorems

Keywords
Law of the iterated logarithm random field trimmed sums

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Liu, Wei-Dong; Lin, Zheng-Yan. Some LIL type results on the partial sums and trimmed sums with multidimensional indices. Electron. Commun. Probab. 12 (2007), paper no. 22, 221--233. doi:10.1214/ECP.v12-1286. https://projecteuclid.org/euclid.ecp/1465224965


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