• 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.

• 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.

• Journal of applied mathematics & informatics
• /
• v.5 no.1
• /
• pp.125-132
• /
• 1998

In this paper we obtain a generalization of Chung's strong law of large numbers to the case of independent fuzzy random variables.

• 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).

• Honam Mathematical Journal
• /
• v.30 no.3
• /
• pp.479-486
• /
• 2008

Let {${\Omega}$, F, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. We study the Hajeck-Renyi-type inequality for p..mixing random variable sequences and obtain the strong law of large numbers by using this inequality. We also consider the strong law of large numbers for weighted sums of ${\tilde{\rho}}$-mixing sequences.

• Communications for Statistical Applications and Methods
• /
• v.9 no.2
• /
• pp.451-457
• /
• 2002

We derive the strong laws of large numbers for weighted averages of partial sums of random variables which are either associated or negatively associated. Our theorems extend and generalize strong law of large numbers for weighted sums of associated and negatively associated random variables of Matula(1996; Probab. Math. Statist. 16) and some results in Birkel(1989; Statist. Probab. Lett. 7) and Matula (1992; Statist. Probab. Lett. 15 ).

• Communications of the Korean Mathematical Society
• /
• v.19 no.4
• /
• pp.765-773
• /
• 2004

In this paper we define the notion of asymptotically quadrant independent random field and derive the strong laws of large numbers for this random field.

• Journal of the Korean Statistical Society
• /
• v.33 no.1
• /
• pp.99-106
• /
• 2004

Let {X, $X_{n}, n\;{\geq}\;1$} be a sequence of identically distributed, negatively associated (NA) random variables and assume that $│X│^{r}$, r > 0, has a finite moment generating function. A strong law of large numbers is established for weighted sums of these variables.

• Journal of the Korean Mathematical Society
• /
• v.45 no.4
• /
• pp.1101-1111
• /
• 2008

Under the condition of h-integrability and appropriate conditions on the array of weights, we establish complete convergence and strong law of large numbers for weighted sums of an array of dependent random variables.