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성수학,Sung, Soo-Hak 배재대학교 자연과학연구소 1999 自然科學論文集 Vol.11 No.1
{f(n)}은 양의 수열로 f(n)$\rightarrow$$\infty$ 이며, {X$_n$,n$\geq1$} 은 쌍별독립인 확률변수 열일 때 정규화된 부분 합 $sum_{i=1}^n$(X$_i$-EX$_i$)/f(n) 이 0에 수렴활 확률이 1이되는 {X$_n$,n$\geq1$} 의 조건을 찾고자 한다. Let {f(n)} be an increasing sequence such that f(n)>0 for each n and f(n)$\rightarrow$$\infty$. Let {X$_n$,n$\geq1$} be a sequence of pairwise independent random variables. In this paper we give sufficient conditions on {X$_n$,n$\geq1$} such that $sum_{i=1}^n$(X$_i$-EX$_i$)/f(n) converges to zero almost surely.
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.
COMPLETE CONVERGENCE FOR WEIGHTED SUMS OF RANDOM ELEMENTS
성수학 대한수학회 2010 대한수학회보 Vol.47 No.2
We obtain a result on complete convergence of weighted sums for arrays of rowwise independent Banach space valued random elements. No assumptions are given on the geometry of the underlying Banach space. The result generalizes the main results of Ahmed et al. [1], Chen et al. [2], and Volodin et al. [14].
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.
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}.
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.
성수학,Sung, Soo-Hak 배재대학교 자연과학연구소 2003 自然科學論文集 Vol.13 No.1
높은 차수의 적률을 갖는 i.i.d. 확률 변수의 가중합에 대한 강대수 법칙을 유도한다. 또한 Sung (2001)의 결과 중 하나를 확장한다. Strong laws of large numbers are established for the weighted sums of i.i.d. random variables which have higher order moment condition. One of the results of Sung(2001) is extended.
성수학,김성수,이규봉,Sung, Soo-Hak,Kim, Sung-Soo,Lee, Gyou-Bong 배재대학교 자연과학연구소 1996 自然科學論文集 Vol.8 No.2
Let {X,$X_n$,n$\geq$1} be i.i.d. random variables with mean zero and {$a_ni$, 1$\leq$i$\leq$n,n$\geq$1} a triangular array of constants. In this paper we give sufficient conditions on X and {$a_ni$} such that $sum_{i=1}^n$$a_{ni}$$X_i$ converges to zero almostly surely. {X,$X_n$,n$\geq$1}은 독립이고 평균이 영으로 같은 확률분포를 갖는 확률변수 열이고, {$a_ni$, 1$\leq$i$\leq$n,n$\geq$1}은 수열일 때 가중합 $sum_{i=1}^n$$a_{ni}$$X_i$가 0에 확률 1로 수렴할 충분조건을 제시한다.
성수학,Sung, Su-Hak 배재대학교 자연과학연구소 2006 自然科學論文集 Vol.17 No.1
확률변수의 랜덤 가중합에 대한 완전수렴 정리를 얻는다. A complete convergence theorem for randomly weighted sums of random variables is obtained. No conditions are imposed on the joint distributions of the random variables.