On the weak law of large numbers for double adapted arrays of random elements in p-uniformly smooth Banach space

被引：0
作者：
Van Quang N. [1 ]
Thuan N.T. [1 ]
机构：
[1] Department of Mathematics, Vinh University, Nghe An
来源：
Lobachevskii Journal of Mathematics | 2009年 / 30卷 / 2期
关键词：
Arrays of martingale differences; Convergence in probability; Double adapted array of random elements; P-uniformly smooth Banach space; Sum of i.i.d. random elements; Weak law of large numbers;
D O I：
10.1134/S1995080209020097
中图分类号：
学科分类号：
摘要：
The aim of this paper is to establish the weak law of large numbers with and wihtout random indices for double arrays of random elements of p-uniformly smooth Banach space. Our result is more general and stronger than some well-known ones. © 2009 Pleiades Publishing, Ltd.
引用
收藏
页码：159 / 167
页数：8
相关论文
共 11 条
  • [1] Chow Y.S., Teicher H., Probability Theory: Independence, Interchangeability, Martingales, (1978)
  • [2] Adler A., Rosalsky A., Volodin A., Weak laws with random indices for arrays of random elements in Rademacher type p Banach spaces, J. Theoret. Probab., 3, (1997)
  • [3] Hall P., Heyde C.C., Martingale Limit Theory and Its Application, (1980)
  • [4] Hong D.H., Ordonez M.C., Sung S.H., Volodin A.I., On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces, Statist. and Probal. Lett., 46, (2000)
  • [5] Hong D.H., Volodin A.I., Marcinkiewicz-type law of large numbers for double arrays, J. Korean Math. Soc., 36, (1999)
  • [6] Hong D.H., Cabrera M.O., Sung S.H., Volodin A., On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces, Statist. Probab. Lett., 46, 2, (2000)
  • [7] Quang N.V., Son L.H., On the weak law of large numbers for senquences of Banach space valued random elements, Bull. Korean Math. Soc., 43, 3, (2006)
  • [8] Quang N.V., Huy N.N., Weak law of large numbers for adapted double arrays of random variables, J. KoreanMath. Soc., 45, 3, (2008)
  • [9] Quang N.V., Huan N.V., On the weak law of large numbers for double arrays of Banach space valued randomelements, Journal of Probability and Statistical Science, 6, 2, pp. 125-134, (2008)
  • [10] Rosalsky A., Thanh L.V., Strong and weak laws of large numbers for double sum of independent random elements in Rademacher type p Banach spaces, Stochastic Analysis and Applications, 24, (2006)
12