• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권3호
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• 대한수학회지
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• 제45권1호
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• pp.289-300
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• 2008

For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.

• 대한수학회지
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• 제56권2호
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• pp.457-473
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• 2019

In this paper, we investigate weak laws of large numbers for weighted coordinatewise pairwise negative quadrant dependence random vectors in Hilbert spaces in the case that the decay order of tail probability is r for some 0 < r < 2. Moreover, we extend results concerning Pareto-Zipf distributions and St. Petersburg game.

• 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$^{p}$.

• 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.

• Communications for Statistical Applications and Methods
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• 제16권3호
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• pp.529-540
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• 2009

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.

• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.299-303
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• 1998

In this paper weak laws of large numbers are obtained for random variables in $L^{1}(R)$ which satisfy a compact uniform integrability condition.

• 한국지능시스템학회논문지
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• 제14권7호
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• pp.852-856
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• 2004

이 논문에서는 퍼지 랜덤 변수의 합에 대한 약한 대수의 법칙을 일반화로서, 컴팩트 일양 적분 가능한 수준 연속 퍼지 랜덤 변수의 가중 합이 약 수렴하기 위한 동치 조건을 구하였다.

• 대한수학회보
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• 제47권3호
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• pp.467-482
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• 2010

For a double array of random elements {$V_{mn};m{\geq}1,\;n{\geq}1$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which $k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i=1}}\sum{{u_n}\atop{i=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in $L_r$ (0 < r < 2). The weak law results provide conditions for $k_{mn}^{-\frac{1}{r}}\sum{{T_m}\atop{i=1}}\sum{{\tau}_n\atop{j=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in probability where {$T_m;m\;{\geq}1$} and {${\tau}_n;n\;{\geq}1$} are sequences of positive integer-valued random variables, {$k_{mn};m{{\geq}}1,\;n{\geq}1$} is an array of positive integers. The sharpness of the results is illustrated by examples.

• 한국콘텐츠학회논문지
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• 제6권5호
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• pp.29-34
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• 2006

본 연구에서는, Banach 공간의 값을 갖는 확률요소들의 합 $S_n=\sum_{i=1}^nV-i$ 수렴하는 경우에, Tail 합 $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$에 대한 대수의 법칙을 고찰하여 $S_n$이 하나의 확률변수 S로 수렴하는 속도를 연구한다. 좀 더 구체적으로 말하자면, 확률변수들의 Tail 합과 확률요소들의 Tail 합에 대한 극한 성질의 유사성을 연구하여, Banach 공간에서 독립인 확률요소들의 Tail 합에 대한 약 대수의 법칙과 하나의 수렴법칙이 동등함을 기술하는 기존의 정리를 다른 대체적인 방법으로 증명한다.