• Journal of the Chungcheong Mathematical Society
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• v.22 no.3
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• pp.507-517
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• 2009

We prove a functional central limit theorem for a linear random field generated by negatively associated multi-dimensional random variables. Under finite second moment condition we extend the result in Kim, Ko and Choi[Kim,T.S, Ko,M.H and Choi, Y.K.,2008. The invariance principle for linear multi-parameter stochastic processes generated by associated fields. Statist. Probab. Lett. 78, 3298-3303] to the negatively associated case.

• Journal of applied mathematics & informatics
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• v.1 no.1
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• pp.31-42
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• 1994

In this paper we investigate an functional central limit theorem for a nonstatioary d-parameter array of associated random variables applying the crite-rion of the tightness condition in Bickel and Wichura[1971]. Our results imply an extension to the nonstatioary case of invariance principle of Burton and Kim(1988) and analogous results for the d-dimensional associated random measure. These re-sults are also applied to show a new functional central limit theorem for Poisson cluster random variables.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.801-811
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• 1996

Let $Z^d$ denote the set of all d-tuples of integers$(d \geq 1, a positive integer)$. The points in $Z^d$ will be denoted by $\underline{m},\underline{n}$, etc., or sometime, when necessary, more explicitly by $(m_1, m_2, \cdots, m_d)$, $(n_1, n_2, \cdots, n_d)$ etc. $Z^d$ is partially ordered by stipulating $\underline{m} \underline{<}\underline{n} iff m_i \leq n_i$ for each i, $1 \leq i \leq d$.