• 대한수학회논문집
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• 제13권1호
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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.

• 대한수학회논문집
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• 제12권2호
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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.

• 대한수학회지
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• 제39권1호
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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.

• 대한수학회논문집
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• 제10권3호
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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.

• 대한수학회보
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• 제35권2호
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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.

• Communications for Statistical Applications and Methods
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• 제2권2호
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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.

• Journal of the Korean Statistical Society
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• 제24권1호
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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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• 제8권1호
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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.

• East Asian mathematical journal
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• 제30권1호
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• pp.31-50
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• 2014

In this paper we establish limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of strictly stationary and linearly positive quadrant dependent (LPQD) or linearly negative quadrant dependent (LNQD) random sequences.

• 대한수학회논문집
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• 제11권1호
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• pp.265-272
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• 1996

In this note we prove a functional central limit theorem for linearly positive quadrant dependent(LPQD) random fields, satisfying some assumption on covariances and the moment condition $\sup_{n \in \Zeta^d} E$\mid$S_n$\mid$^{2+\rho} < \infty$ for some $\rho > 0$. We also apply this notion to random measures.