• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.37-49
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• 1999

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.151-158
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• 1998

In this note we derive inequalities of linearly positive quadrant dependent random variables and obtain a strong law of large numbers for linealy positive quardant dependent random variables. Our results imply an extension of Birkel's strong law of large numbers for associated random variables to the linear positive quadrant dependence case.

• Communications of the Korean Mathematical Society
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• v.12 no.2
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• pp.411-418
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• 1997

In this note we prove a functional central limit theorem for nonstationary linearly positive quadrant dependent random fields. We extend it to the case of random measures.

• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.707-714
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• 1995

In this note, we extend the concepts of linearly positive quadrant dependence to the random vectors and prove a functional central limit theorem for positively quadrant dependent sequence of $R^d$-valued or separable Hilbert space valued random elements which satisfy a covariance summability condition. This result is an extension of a functional central limit theorem for weakly associated random vectors of Burton et al. to positive quadrant dependence case.

• Journal of the Korean Mathematical Society
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• v.39 no.1
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• pp.119-126
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• 2002

For a stationary multivariate linear process of the form X$_{t}$ = (equation omitted), where {Z$_{t}$ : t = 0$\pm$1$\pm$2ㆍㆍㆍ} is a sequence of stationary linearly positive quadrant dependent m-dimensional random vectors with E(Z$_{t}$) = O and E∥Z$_{t}$∥ $^2$< $\infty$, we prove a central limit theorem.theorem.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.279-292
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• 1998

We derive maximal inequalities of linearly positive quadrant dependent (LPQD) random variables for d = 1,2. With an application we also obtain the weak convergence for 2-parameter arrays of LPQD random variables.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.249-256
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• 1995

In this note we prove an invariance principle for strictly stationary linear positive quadrant dependent sequences, satifying some assumption on the covariance structure, $0 < \sum Cov(X_1,X_j) < \infty$. This result is an extension of Burton, Dabrowski and Dehlings' invariance principle for weakly associated sequences to LPQD sequences as well as an improvement of Newman's central limit theorem for LPQD sequences.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.350-357
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• 1995

In this note, we obtain the central limit theorem for linearly positive quadrant dependent random fields satisfying some assumptions on the covariances and the moment condition $supE\mid X_i\mid^3\;<{\infty}$ The proofs are similar to those of a central limit theorem for associated random field of Cox and Grimmett.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.797-804
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• 1999

In this paper we derive the almost sure convergence of weighted sums of 2-dimensional arrays of random variables which are either pairwise positive quadrant dependent or associated. Our re-sults imply and extension of Etemadi's(1983) strong laws of large numbers for weighted sums of nonnegative random variables to the 2-dimensional case.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.153-158
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• 2001

A central limit theorem is obtained for stationary linear process of the form -Equations. See Full-text-, where {$\varepsilon$$_{t}$} is a strictly stationary sequence of linearly positive quadrant dependent random variables with E$\varepsilon$$_{t}$=0, E$\varepsilon$$^2$$_{t}$<$\infty$ and { $a_{j}$} is a sequence of real numbers with -Equations. See Full-text- we also derive a functional central limit theorem for this linear process.ocess.s.