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On limiting behavior for arrays of rowwise negatively orthant dependent random variables
Andrei Volodin,Yong-Feng Wu,Manuel Ordóñez Cabrera 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.1
In this paper, the authors study limiting behavior for arrays of rowwise negatively orthant dependent random variables and obtain some new results which extend and improve the corresponding theorems by Hu, Móricz, and Taylor (1989), Taylor, Patterson, and Bozorgnia (2002) and Wu and Zhu (2010).
A note on the exponential inequality for a class of dependent random variables
성수학,Patchanok Srisuradetchai,Andrei Volodin 한국통계학회 2011 Journal of the Korean Statistical Society Vol.40 No.1
An exponential inequality is established for a random variable with the finite Laplace transform. Using this inequality, we obtain an exponential inequality for identically distributed acceptable random variables (a class of random variables introduced in Giuliano Antonini, Kozachenko, and Volodin (2008) which includes negatively dependent random variables). Our result improves the corresponding ones in Kim and Kim (2007), Nooghabi and Azarnoosh (2009), Sung (2009), Xing (2009), Xing and Yang (2010) and Xing, Yang, Liu,and Wang (2009). Our method is much simpler than those in the literature.
ON THE RATE OF COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF ARRAYS OF RANDOM ELEMENTS
Sung, Soo-Hak,Volodin Andrei I. Korean Mathematical Society 2006 대한수학회지 Vol.43 No.4
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 $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.
MARCINKIEWICZ-TYPE LAW OF LARGE NUMBERS FOR DOUBLE ARRAYS
Hong, Dug-Hun,Volodin, Andrei I. Korean Mathematical Society 1999 대한수학회지 Vol.36 No.6
Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.
On the rate of complete convergence for weighted sums of arrays of random elements
성수학,Andrei I. Volodin 대한수학회 2006 대한수학회지 Vol.43 No.4
Let {V_{nk}, k ge 1, nge 1} be an array of rowwise independent random elements which are stochasticallydominated by a random variable X with E|X|^{frac{alpha}{gamma}+theta}log^rho (|X|) <infty for somerho>0, alpha>0, gamma>0, theta>0 such that theta+alpha/gamma<2.Let {a_{nk}, k ge 1, nge 1} be an array of suitable constants.A complete convergence result is obtained for the weighted sums of the form sum_{k=1}^infty a_{nk}V_{nk}.
Weak laws of large numbers for arrays under a condition of uniform integrability
성수학,Supranee Lisawadi,Andrei Volodin 대한수학회 2008 대한수학회지 Vol.45 No.1
For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature. For an array of dependent random variables satisfying a new notion of uniform integrability, weak laws of large numbers are obtained. Our results extend and sharpen the known results in the literature.
ON CONVERGENCE OF SERIES OF INDEPENDENTS RANDOM VARIABLES
Sung, Soo-Hak,Volodin, Andrei-I. Korean Mathematical Society 2001 대한수학회보 Vol.38 No.4
The rate of convergence for an almost surely convergent series $S_n={\Sigma^n}_{i-1}X_i$ of independent random variables is studied in this paper. More specifically, when S$_{n}$ converges almost surely to a random variable S, the tail series $T_n{\equiv}$ S - S_{n-1} = {\Sigma^\infty}_{i-n} X_i$ is a well-defined sequence of random variables with T$_{n}$ $\rightarrow$ 0 almost surely. Conditions are provided so that for a given positive sequence {$b_n, n {\geq$ 1}, the limit law sup$_{\kappa}\geqn | T_{\kappa}|/b_n \rightarrow$ 0 holds. This result generalizes a result of Nam and Rosalsky [4].
STRONG LIMIT THEOREMS FOR WEIGHTED SUMS OF NOD SEQUENCE AND EXPONENTIAL INEQUALITIES
Wang, Xuejun,Hu, Shuhe,Volodin, Andrei I. Korean Mathematical Society 2011 대한수학회보 Vol.48 No.5
Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.
On limiting behavior for arrays of rowwise negatively orthant dependent random variables
Wu, Yongfeng,Ordonez Cabrera, Manuel,Volodin, Andrei 한국통계학회 2013 Journal of the Korean Statistical Society Vol.42 No.1
In this paper, the authors study limiting behavior for arrays of rowwise negatively orthant dependent random variables and obtain some new results which extend and improve the corresponding theorems by Hu, M$\acute{o}$ricz, and Taylor (1989), Taylor, Patterson, and Bozorgnia (2002) and Wu and Zhu (2010).
Strong limit theorems for weighted sums of NOD sequence and exponential inequalities
Xuejun Wang,Shuhe Hu,Andrei I. Volodin 대한수학회 2011 대한수학회보 Vol.48 No.5
Some properties for negatively orthant dependent sequence are discussed. Some strong limit results for the weighted sums are obtained, which generalize the corresponding results for independent sequence and negatively associated sequence. At last, exponential inequalities for negatively orthant dependent sequence are presented.