• Journal of the Korean Statistical Society
• /
• v.23 no.2
• /
• pp.523-528
• /
• 1994

The purpose of this note is to provide a general weak law of randomly indexed partial sums for arrays.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.1
• /
• pp.75-83
• /
• 2011

In this paper the Baum-Katz law of large numbers for negatively orthant dependent random variables is studied. The complete convergence of negatively orthant dependent random variables under some conditions of uniform integrablity is also obtained.

• The Journal of the Korea Contents Association
• /
• v.6 no.5
• /
• pp.29-34
• /
• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• Journal of applied mathematics & informatics
• /
• v.16 no.1_2
• /
• pp.419-427
• /
• 2004

In this paper we establish the Hajeck-Renyi type inequality and derive the strong law of large numbers for asymptotically quadrant sub-independent random variables.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.13 no.6
• /
• pp.754-758
• /
• 2003

The present paper establishes a strong law of large numbers for sums of tight fuzzy random variables as a generalization of SLLN for sums of independent and identically distributed fuzzy random variables.

• Communications of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.151-161
• /
• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1997.10a
• /
• pp.207-213
• /
• 1997

In this paper, we generalize Kolmogorov' strong law of large numbers to the the case of independent fuzzy random variables.

• Communications of the Korean Mathematical Society
• /
• v.20 no.1
• /
• pp.161-168
• /
• 2005

In this paper, we obtain strong law of large numbers for linear process generated by asymptotically linear negative quadrant dependence processes.

• Proceedings of the Korean Statistical Society Conference
• /
• 2001.11a
• /
• pp.137-141
• /
• 2001

We can obtain SLLN's for fuzzy random variables with respect to the new metric $d_s$ on the space F(R) of fuzzy numbers in R. In this paper, we obtain a SLLN for convex tight random elements taking values in F(R).

• Communications of the Korean Mathematical Society
• /
• v.16 no.2
• /
• pp.291-296
• /
• 2001

For randomly indexed sums of the form (Equation. See Full-text), where {X(sub)ni, i$\geq$1, n$\geq$1} are random variables, {N(sub)n, n$\geq$1} are suitable conditional expectations and {b(sub)n, n$\geq$1} are positive constants, we establish a general weak law of large numbers. Our result improves that of Hong [3].