• Title/Summary/Keyword: uniformly random numbers.

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CONVERGENCE OF DOUBLE SERIES OF RANDOM ELEMENTS IN BANACH SPACES

  • Tien, Nguyen Duy;Dung, Le Van
    • Journal of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.1053-1064
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    • 2012
  • For a double array of random elements $\{X_{mn};m{\geq}1,n{\geq}1\}$ in a $p$-uniformly smooth Banach space, $\{b_{mn};m{\geq}1,n{\geq}1\}$ is an array of positive numbers, convergence of double random series ${\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}X_{mn}$, ${\sum}^{\infty}_{m=1}{\sum}^{\infty}_{n=1}b^{-1}_{mn}X_{mn}$ and strong law of large numbers $$b^{-1}_{mn}\sum^m_{i=1}\sum^n_{j=1}X_{ij}{\rightarrow}0$$ as $$m{\wedge}n{\rightarrow}{\infty}$$ are established.

SOME NOTES ON STRONG LAW OF LARGE NUMBERS FOR BANACH SPACE VALUED FUZZY RANDOM VARIABLES

  • Kim, Joo-Mok;Kim, Yun Kyong
    • Korean Journal of Mathematics
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    • v.21 no.4
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    • pp.383-399
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    • 2013
  • In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

Weak convergence for weighted sums of level-continuous fuzzy random variables (수준 연속인 퍼지 랜덤 변수의 가중 합에 대한 약 수렴성)

  • Kim, Yun-Kyong
    • Journal of the Korean Institute of Intelligent Systems
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    • v.14 no.7
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    • pp.852-856
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    • 2004
  • The present paper establishes a necessary and sufficient condition for weak convergence for weighted sums of compactly uniformly integrable level-continuous fuzzy random variables as a generalization of weak laws of large numbers for sums of fuzzy random variables.

STRONG LAWS OF LARGE NUMBERS FOR RANDOM UPPER-SEMICONTINUOUS FUZZY SETS

  • Kim, Yun-Kyong
    • Bulletin of the Korean Mathematical Society
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    • v.39 no.3
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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.

Weak laws of large numbers for weighted sums of Banach space valued fuzzy random variables

  • Kim, Yun Kyong
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • v.13 no.3
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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.

Weak Laws of Large Numbers for Weighted Sums of Fuzzy Random Variables

  • Hyun, Young-Nam;Kim, Yun-Kyong;Kim, Young-Ju;Joo, Sang-Yeol
    • Communications for Statistical Applications and Methods
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    • v.16 no.3
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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.

STRONG CONVERGENCE FOR WEIGHTED SUMS OF FUZZY RANDOM VARIABLES

  • Kim, Yun-Kyong
    • Proceedings of the Korean Statistical Society Conference
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    • 2003.10a
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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$^{p}$.

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Random Elements in $L^1(R)$ and Kernel Density Estimators

  • Lee, Sung-Ho;Lee, Robert -Taylor
    • Journal of the Korean Statistical Society
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    • v.22 no.1
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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.

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