• Bulletin of the Korean Mathematical Society
• /
• v.38 no.1
• /
• pp.55-63
• /
• 2001

In this paper, we derive a general strong law of large numbers and a general weak law of large number for normed weighted sums of pairwise negative quadrant dependent random variables with the common distribution function.

• Journal of applied mathematics & informatics
• /
• v.30 no.1_2
• /
• pp.327-336
• /
• 2012

Let {$X_{ni}$, $i{\geq}1$, $n{\geq}1$} be an array of rowwise and pairwise negatively quadrant dependent random variables with mean zero, {$a_{ni}$, $i{\geq}1$, $n{\geq}1$} an array of weights and {$b_n$, $n{\geq}1$} an increasing sequence of positive integers. In this paper we consider some results concerning complete convergence of ${\sum}_{i=1}^{bn}a_{ni}X_{ni}$.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.3
• /
• pp.615-623
• /
• 2013

In this paper we establish a central limit theorem for weighted sums of $Y_n={\sum_{i=1}^{n}}a_n,_iX_i$, where $\{a_{n,i},\;n{\in}N,\;1{\leq}i{\leq}n\}$ is an array of nonnegative numbers such that ${\sup}_{n{\geq}1}{\sum_{i=1}^{n}}a_{n,i}^2$ < ${\infty}$, ${\max}_{1{\leq}i{\leq}n}a_{n,i}{\rightarrow}0$ and $\{X_i,\;i{\in}N\}$ is a sequence of linear negatively quadrant dependent random variables with $EX_i=0$ and $EX_i^2$ < ${\infty}$. Using this result we will obtain a central limit theorem for partial sums of linear processes.

• Honam Mathematical Journal
• /
• v.21 no.1
• /
• pp.149-156
• /
• 1999

Let $\{X_n,\;n{\geq}1\}$ be a sequence of pairwise negative quadrant dependent (NQD) random variables which are stochastically dominated by X. Let $\{a_n,\;n{\geq}1\}$ and $\{b_n,\;n{\geq}1\}$ be sequences of constants such that $a_n>0$ and $0. In this note a weak law of large number of the form $({\sum}_{j=1}^na_jX_j-{\nu}_n)/b_n\rightarrow\limits^p0$ is established, where $\{{\nu}_n,\;n{\geq}1\}$ is a suitable sequence.

• Honam Mathematical Journal
• /
• v.33 no.2
• /
• pp.163-171
• /
• 2011

In this paper we provide extensions of the Marcinkiewicz Zygmund laws of large numbers for i.i.d random variables with multidimensional indices to the case of negatively dependent random fields.

• Journal of the Korean Statistical Society
• /
• v.29 no.3
• /
• pp.261-268
• /
• 2000

Let {Xn,n$\geq$1} be a sequence of pairwise negative quadrant dependent(NQD) random variables and let {an,n$\geq$1} and {bn,n$\geq$1} be sequencesof constants such that an$\neq$0 and 0$\infty$. In this note, for pairwise NQD random varibles, a general weak law of alrge numbers of the form(∑│aj│Xj-$\upsilon$n)/bnlongrightarrow0) is established, where {νn,n$\geq$1} is a suitable sequence. AMS 2000 subject classifications ; 60F05

• Journal of the Korean Mathematical Society
• /
• v.43 no.6
• /
• pp.1325-1338
• /
• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences of negatively orthant dependent random variables ${X_n,\;n{\geq}1}$, the conditions for strong law of large number of ${\sum}^{k_n}_{i=1}a_{ni}X_i$ are given. Both cases $k_n{\uparrow}{\infty}\;and\;k_n={\infty}$ are treated.

• 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.

• Honam Mathematical Journal
• /
• v.31 no.4
• /
• pp.505-513
• /
• 2009

Let {$X_k;k{\in}N^d$} be centered and identically distributed random field which is asymptotically negative dependent in a certain case. In this note we prove that for $p{\alpha}$ > 1 and ${\alpha}$ > ${\frac{1}{2}}$ $E{\mid}X_1{\mid}^p(log^+{\mid}X_1{\mid}^{d-1})$ < ${\infty}$ if and only if ${\sum}_n{\mid}n{\mid}^{p{\alpha}-2}P$($max_{1{\leq}k{\leq}n{\mid}S_k{\mid}}$ > ${\epsilon}{\mid}n{\mid}$) < ${\infty}$ for all ${\epsilon}$ > 0, where log$^+$x = max{1,log x}.