Weak Laws of Large Numbers of Cesaro Summation for Random Arrays
Main Article Content
Abstract
In this paper, we establish weak laws of large numbers with or without random indices for Cesaro summation for random arrays of random elements in Banach spaces. Our results are more general and stronger than some well-known ones. AMS Subject classification 2000: 60B11, 60B12, 60F05, 60G42.
Keywords: p-uniformly smooth Banach space, double arrays of random elements, double arrays, random indices, weak laws of large numbers.
References
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[2] M. Ordonez Cabrera, Limit theorems for randomly weighted sums of random elements in normed linear spaces, Journalof Multivariate Analysis 25 (1988), no. 1, 139-145.
[3] A. Adler, A. Rosalsky and R. L. Taylor, A weak law for normed weighted sums of random elements in Rademacher typep Banach spaces, Journal of Multivariate Analysis 37 (1991), no. 2, 259-268.
[4] S. H. Sung, T.C. Hu and A.I. Volodin, On the weak laws with random indices for partial sums for arrays of randomelements in martingale type p Banach spaces, Bull.Korean.Soc. 43 (2006), no. 3, 543-549.
[5] L.V. Dung, Weak law of large numbers for double arrays of random elements in Banach spaces, Acta MathematicaVietnamica 35 (2010), 387-398.
[6] F. S. Scalora, Abstract martingale convergence theorems, Pacific J. Math. 11 (1961), 347-374.
[7] J. Hoffmann-Jorgensen and G. Pisier, The law of large numbers and the central limit theorem in Banach spaces, Annalsof Probability 4 (1976), no. 4, 587-599.