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ON THE WEAK LAW OF LARGE NUMBERS FOR SEQUENCES OF BANACH SPACE VALUED RANDOM ELEMENTS
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 Title & Authors
ON THE WEAK LAW OF LARGE NUMBERS FOR SEQUENCES OF BANACH SPACE VALUED RANDOM ELEMENTS
Quang, Nguyen Aan; Son, Le-Hong;
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 Abstract
We establish a weak law of large numbers for sequence of random elements with values in p-uniformly smooth Banach space. Our result is more general and stronger than some well-known ones.
 Keywords
weak law of large numbers;martingale;p-uniformly smooth Banach space;
 Language
English
 Cited by
1.
On the weak law of large numbers for double adapted arrays of random elements in p-uniformly smooth Banach space, Lobachevskii Journal of Mathematics, 2009, 30, 2, 159  crossref(new windwow)
2.
A characterization of p-uniformly smooth Banach spaces and weak laws of large numbers for d-dimensional adapted arrays, Sankhya A, 2010, 72, 2, 344  crossref(new windwow)
 References
1.
A. Adler, A Rosalsky, and A. I. Volodin, Weak laws with random indices for arrays of random elements in Rademacher type p Banach spaces. J. Theoret. Probab. (1997), no. 3, 605-623

2.
P. Hall and C. C. Heyde, Martingale limit theory and its application, Academic Press, New York, 1980

3.
D. H. Hong, M. Ordonez Cabrera, S. H. Sung, and A. I. Volodin, On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces, Statist. Probab. Lett. 46 (2000), no. 2, 177-185 crossref(new window)

4.
N. V. Hung and N. D. Tien, On the convergence of weighted sums of martingale differences, Acta Math. Vietnam. 13 (1988), no. 1, 43-53

5.
M. Loeve, Probability Theory I, 4th ed., Graduate Texts in Mathematics, Vol. 45, Springer-Verlag, Berlin and New York, 1977

6.
S. H. Sung, Weak law of large numbers for arrays of random variables, Statist. Probab. Lett. 42 (1998), no. 3, 293-298

7.
W. A. Woyczynski, Geometry and martingale in Banach spaces II. Independent increments, Marcel Dekker, Press New York, 1978