• Communications for Statistical Applications and Methods
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• 제15권6호
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• pp.959-967
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• 2008

In this paper we show the weak convergence of the linear random(multistochastic process) field generated by identically distributed 2-parameter array of associated random variables. Our result extends the result in Newman and Wright (1982) to the linear 2-parameter processes as well as the result in Kim and Ko (2003) to the 2-parameter case.

• 대한수학회지
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• 제42권1호
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• pp.153-169
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• 2005

A fuzzy stochastic differential equation contains a fuzzy valued diffusion term which is defined by stochastic integral of a fuzzy process with respect to 1-dimensional Brownian motion. We prove the existence and uniqueness of the solution for fuzzy stochastic differential equation under suitable Lipschitz condition. To do this we prove and use the maximal inequality for fuzzy stochastic integrals. The results are illustrated by an example.

• 충청수학회지
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• 제22권3호
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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.

• 대한수학회지
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• 제37권3호
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• pp.463-471
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• 2000

A central limit theorem is obtained for stationary linear process Xt = aj$\varepsilon$t-j, where {$\varepsilon$t} a strictly stationary associated sequence with Et < and {aj} is a sequence of real numbers with <. A functional central limit theorem is also derived.

• Journal of the Korean Statistical Society
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• 제31권3호
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• pp.369-378
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• 2002

Strong laws of large numbers for weighted sums of asymptotically almost negatively associated(AANA) sequence are proved by our generalized maximal inequality for AANA random variables at a crucial step.

• 충청수학회지
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• 제32권3호
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• pp.327-336
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• 2019

In this paper, the weak laws of large numbers for sums of asymptotically almost negatively associated random vectors in Hilbert spaces are investigated. Some results in Hien and Thanh ([3]) are generalized to asymptotically almost negatively random vectors in Hilbert space.

• 대한수학회논문집
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• 제26권1호
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.615-623
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• 2001

A functional central limit theorem is obtained for a stationary multivariate linear process of the form (no abstract. see full-text) where{ $Z_{t}$} is a sequence of strictly stationary m-dimensional negatively associated random vectors with E $Z_{t}$=O and E∥ $Z_{t}$∥$^2$<$\infty$ and { $A_{u}$} is a sequence of coefficient matrices with (no abstract. see full-text) and (no abstract. see full-text).text).).

• 호남수학학술지
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• 제31권4호
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• pp.505-513
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• 2009

Let {$X_k;k{\in}N^d$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $p{\alpha}$ > 1 and ${\alpha}$ > ${\frac{1}{2}}$ $E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})$ < ${\infty}$ if and only if ${\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P$($max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}$ > ${\epsilon}{\mid}n{\mid}$) < ${\infty}$ for all ${\epsilon}$ > 0, where log$^+$x = max{1,log x}.

• 대한수학회지
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• 제59권5호
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• pp.927-944
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• 2022

Let $\vec{p}{\in}(0,\;1]^n$ be an n-dimensional vector and A a dilation. Let $H^{\vec{p}}_A(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space defined via the radial maximal function. Using the known atomic characterization of $H^{\vec{p}}_A(\mathbb{R}^n)$ and establishing a uniform estimate for corresponding atoms, the authors prove that the Fourier transform of $f{\in}H^{\vec{p}}_A(\mathbb{R}^n)$ coincides with a continuous function F on ℝⁿ in the sense of tempered distributions. Moreover, the function F can be controlled pointwisely by the product of the Hardy space norm of f and a step function with respect to the transpose matrix of A. As applications, the authors obtain a higher order of convergence for the function F at the origin, and an analogue of Hardy-Littlewood inequalities in the present setting of $H^{\vec{p}}_A(\mathbb{R}^n)$.