http://chineseinput.net/에서 pinyin(병음)방식으로 중국어를 변환할 수 있습니다.
변환된 중국어를 복사하여 사용하시면 됩니다.
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 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].
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}.
성수학,Tien-Chung Hu,Andrei I. Volodin 대한수학회 2006 대한수학회보 Vol.43 No.3
Sung et al. [13] obtained a WLLN (weak law of largenumbers) for the arrayfXni ;un i vn ;n 1g of random vari-ables under a Cesaro type condition, wherefun 1 ;n 1g andfvn + 1 ;n 1g are two sequences of integers. In this paper, weextend the result of Sung et al. [13] to a martingale typep Banachspace.
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.
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 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 $\sum{^\infty_k_=_1}\;a_{nk}V_{nk}$.
Sung, Soo-Hak,Hu, Tien-Chung,Volodin, Andrei I. Korean Mathematical Society 2006 대한수학회보 Vol.43 No.3
Sung et al. [13] obtained a WLLN (weak law of large numbers) for the array $\{X_{{ni},\;u_n{\leq}i{\leq}v_n,\;n{\leq}1\}$ of random variables under a Cesaro type condition, where $\{u_n{\geq}-{\infty},\;n{\geq}1\}$ and $\{v_n{\leq}+{\infty},\;n{\geq}1\}$ large two sequences of integers. In this paper, we extend the result of Sung et al. [13] to a martingale type p Banach space.