• 대한수학회논문집
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• 제14권3호
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• pp.581-595
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• 1999

In the present paper we provide a short of the uni-form CLT for the function-indexed martingale difference process under the uniformly integrable entropy by establishing a maximal inequality.

• 대한수학회보
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• 제47권1호
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• pp.39-51
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• 2010

In this paper we consider the uniform central limit theorem for a martingale-difference array of a function-indexed stochastic process under the uniformly integrable entropy condition. We prove a maximal inequality for martingale-difference arrays of process indexed by a class of measurable functions by a method as Ziegler [19] did for triangular arrays of row wise independent process. The main tools are the Freedman inequality for the martingale-difference and a sub-Gaussian inequality based on the restricted chaining. The results of present paper generalizes those of Ziegler [19] and other results of independent problems. The results also generalizes those of Bae and Choi [3] to martingale-difference array of a function-indexed stochastic process. Finally, an application to classes of functions changing with n is given.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제7권2호
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• pp.137-143
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• 2000

In this paper, we define the uniformly sequence for the vector valued McShand-Stieltjes integrable functions and prove the dominated convergence theorem for the McShand-Stieltjes integrable functions.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 추계 학술발표회 논문집
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• pp.183-188
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• 2003

In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• Journal of the Korean Statistical Society
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• 제22권1호
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• pp.83-91
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• 1993

Random elements in $L^1(R)$ and some properties of $L^1(R)$ space are investigated with application to kernel density estimators. A weak law of large numbers for compact uniformly integrable random elements is introduced for further application.

• Journal of the Korean Statistical Society
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• 제24권2호
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• pp.273-280
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• 1995

This paper gives a generalization of an $L_1$-convergence theorem for dependent processes due to Andrews (1988) and also a probability convergence theorem.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.621-640
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• 2022

The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.215-220
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• 2002

In this paper, we establish weak laws of large numbers for weighted sums of convex-compactly uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• 대한수학회보
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• 제39권3호
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• pp.511-526
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• 2002

In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.

• 대한수학회보
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• 제41권2호
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.