• 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.

• 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.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.299-305
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• 2003

The central limit theorems are obtained for stationary linear processes of the form Xt = (equation omitted), where {$\varepsilon$t} is a strictly stationary sequence of random variables which are either linearly positive quad-rant dependent or associated and {aj} is a sequence of .eat numbers with (equation omitted).

• Journal of the Korean Statistical Society
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• 제31권4호
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• pp.483-490
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• 2002

A weak convergence is obtained for a linear process of the form (equation omitted) where {$\varepsilon$$_{t}$ } is a strictly stationary sequence of associated random variables with E$\varepsilon$$_{t}$ = 0 and E$\varepsilon$$^{^2}$$_{t}$ < $\infty$ and {a $_{j}$ } is a sequence of real numbers with (equation omitted). We also apply this idea to the case of linearly positive quadrant dependent sequence.

• 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.

• 대한수학회지
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• 제49권2호
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• pp.223-233
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• 2012

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

• 대한수학회논문집
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• 제9권4호
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• pp.951-959
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• 1994

A sequence ${X_j : j \geq 1}$ of random variables is said to be pairwise positive quadrant dependent (pairwise PQD) if for any real $r-i,r_j$ and $i \neq j$ $$ P{X_i > r_i,X_j > r_j} \geq P{X_i > r_i}P{X_j > r_j} $$ (see [8]) and a sequence ${X_j : j \geq 1}$ of random variables is said to be associated if for any finite collection ${X_{i(1)},...,X_{j(n)}}$ and any real coordinatewise nondecreasing functions f,g on $R^n$ $$ Cov(f(X_{i(1)},...,X_{j(n)}),g(X_{j(1)},...,X_{j(n)})) \geq 0, $$ whenever the covariance is defined (see [6]). Instead of association Cox and Grimmett's [4] original central limit theorem requires only that positively linear combination of random variables are PQD (cf. Theorem $A^*$).

• 대한수학회지
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• 제43권3호
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• pp.529-538
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• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• 대한수학회보
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• 제47권3호
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• pp.585-592
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• 2010

Let {$\varepsilon_i:-{\infty}$$\infty$} be a strictly stationary sequence of linearly positive quadrant dependent random variables and $\sum\limits\frac_{i=-{\infty}}^{\infty}|a_i|$<$\infty$. In this paper, we prove the precise asymptotics in the law of iterated logarithm for the moment convergence of moving-average process of the form $X_k=\sum\limits\frac_{i=-{\infty}}^{\infty}a_{i+k}{\varepsilon}_i,k{\geq}1$