• Journal of the Korean Mathematical Society
• /
• v.43 no.4
• /
• pp.815-828
• /
• 2006

Let {$V_{nk},\;k\;{\geq}\;1,\;{\geq}\;1$} be an array of rowwise independent random elements which are stochastically dominated by a random variable X with $E\|X\|^{\frac{\alpha}{\gamma}+{\theta}}log^{\rho}(\|X\|)\;<\;{\infty}$ for some ${\rho}\;>\;0,\;{\alpha}\;>\;0,\;{\gamma}\;>\;0,\;{\theta}\;>\;0$ such that ${\theta}+{\alpha}/{\gamma}<2$. Let {$a_{nk},k{\geq}1,n{\geq}1$) be an array of suitable constants. A complete convergence result is obtained for the weighted sums of the form $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.

• 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

• Bulletin of the Korean Mathematical Society
• /
• v.32 no.2
• /
• pp.221-231
• /
• 1995

Let $Z_1, Z_2, \ldots, Z_l$ be random set functions or intergrals. Then it is possible to discuss their products. In the case of random integrals, $Z_i$ is a random set function indexed y a family, $G_i$ say, of real valued functions g on $S_i$ for which the integrals $Z_i(g) = \smallint gdZ_i$ are well defined. If $g_i = \in g_i (i = 1, 2, \ldots, l) and g_1 \otimes \cdots \otimes g_l$ denotes the tensor product $g(s) = g_1(s_1)g_2(s_2) \cdots g_l(s_l) for s = (s_1, s_2, \ldots, s_l) and s_i \in S_i$, then we can defined $Z(g) = (Z_1 \times Z_2 \times \cdots \times Z_l)(g) = Z_1(g_1)Z_2(g_2) \cdots Z_l(g_l)$.

• Communications for Statistical Applications and Methods
• /
• v.16 no.3
• /
• pp.549-556
• /
• 2009

Let $\{(X_{ni}|1{\leq}i{\leq}n,\;n{\geq}1)\}$ be an array of rowwise negatively associated random variables. In this paper we discuss $n^{{\alpha}p-2}h(n)max_{1{\leq}k{\leq}n}|{\sum}_{i=1}^kX_{ni}|/n^{\alpha}{\rightarrow}0$ completely as $n{\rightarrow}{\infty}$ under not necessarily identically distributed with suitable conditions for ${\alpha}$>1/2, 0${\alpha}p{\geq}1$ and a slowly varying function h(x)>0 as $x{\rightarrow}{\infty}$. In addition, we obtain the complete convergence of moving average process based on negative association random variables which extends the result of Zhang (1996).

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1879-1903
• /
• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• ETRI Journal
• /
• v.35 no.4
• /
• pp.714-717
• /
• 2013

Peak power reduction techniques in orthogonal frequency division multiplexing (OFDM) has been an important subject for many researchers for over 20 years. In this letter, we propose a side-information-free technique that is based on the concept of random variable (RV) transformation. The suggested method transforms RVs into other RVs, aiming to reshape the constellation that will consequently produce OFDM symbols with a reduced peak-to-average power ratio. The proposed method has no limitation on the mapping type or the mapping order and has no significant effect on the bit error rate performance compared to other methods presented in the literature. Additionally, the computational complexity does not increase.

• The Pure and Applied Mathematics
• /
• v.11 no.2
• /
• pp.139-147
• /
• 2004

Let {<$\mathds{X}_t$} be an m-dimensional linear process of the form $\mathbb{X}_t\;=\sumA,\mathbb{Z}_{t-j}$ where {$\mathbb{Z}_t$} is a sequence of stationary m-dimensional negatively associated random vectors with $\mathbb{EZ}_t$ = $\mathbb{O}$ and $\mathbb{E}\parallel\mathbb{Z}_t\parallel^2$ < $\infty$. In this paper we prove the central limit theorems for multivariate linear processes generated by negatively associated random vectors.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.18 no.3
• /
• pp.201-207
• /
• 2018

There is no known polynomial time algorithm for random-type quadratic assignment problem(RQAP) that is a NP-complete problem. Therefore the heuristic or meta-heuristic approach are solve the approximated solution for the RQAP within polynomial time. This paper suggests polynomial time algorithm for random type quadratic assignment problem (QAP) with time complexity of $O(n^2)$. The proposed algorithm applies one-to-one matching strategy between ascending order of sum of distance for each location and descending order of sum of quantity for each facility. Then, swap the facilities for reflect the correlation of distances of locations and quantities of facilities. For the experimental data, this algorithm, in spite of $O(n^2)$ polynomial time algorithm, can be improve the solution than genetic algorithm a kind of metaheuristic method.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.127-136
• /
• 2010

For the maximum partial sum of linear process generated by a doubly infinite sequence of identically distributed $\rho$-mixing random variables with mean zeros, a complete convergence is obtained under suitable conditions.