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http://dx.doi.org/10.4134/JKMS.2008.45.3.795

WEAK LAW OF LARGE NUMBERS FOR ADAPTED DOUBLE ARRAYS OF RANDOM VARIABLES  

Quang, Nguyen Van (Department of Mathematics Vinh University)
Hyu, Nguyen Ngoc (Department of Mathematics Vinh University)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.3, 2008 , pp. 795-805 More about this Journal
Abstract
The aim of this paper is to extend the "classical degenerate convergence criterion" and the Feller weak law of large numbers to double adapted arrays of random variables.
Keywords
double adapted array of random variables; weak law of large numbers; convergence in probability; martingale difference; sum of i.i.d. random variables;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 2
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1 D. H. Hong and K. S. Oh, On the weak law of large numbers for arrays, Statist. Probab. Lett. 22 (1995), no. 1, 55-57   DOI   ScienceOn
2 A. Adler, A. Rosalsky, and A. I. Volodin, A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces, Statist. Probab. Lett. 32 (1997), no. 2, 167-174   DOI   ScienceOn
3 S. E. Ahmed, S. H. Sung, and A. I. Volodin, Mean convergence theorem for arrays of random elements in martingale type p Banach spaces, Bull. Inst. Math. Acad. Sinica 30 (2002), no. 2, 89-95
4 Y. S. Chow and H. Teicher, Probability Theory, Independence, interchangeability, martingales. Springer-Verlag, New York-Heidelberg, 1978
5 A. Gut, An extension of Feller's weak law of large numbers, http://www.math.uu.se/research/pub/Gut8.pdf
6 D. H. Hong and S. Lee, A general weak law of large numbers for arrays, Bull. Inst. Math. Acad. Sinica 24 (1996), no. 3, 205-209
7 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   DOI   ScienceOn
8 D. H. Hong and A. I. Volodin, Marcinkiewicz-type law of large numbers for double arrays, J. Korean Math. Soc. 36 (1999), no. 6, 1133-1143
9 P. Hall and C. C. Heyde, Martingale Limit Theory and Its Application, Probability and Mathematical Statistics. Academic Press, Inc. Harcourt Brace Jovanovich, Publishers, New York-London, 1980
10 M. Loeve, Probability Theory. I, Fourth edition. Graduate Texts in Mathematics, Vol. 45. Springer-Verlag, New York-Heidelberg, 1977
11 S. H. Sung, Weak law of large numbers for arrays, Statist. Probab. Lett. 38 (1998), no. 2, 101-105   DOI   ScienceOn
12 S. H. Sung, On the weak laws with random indices for partial sums for arrays of random elements in martingale type p Banach spaces, Bull. Korean Math. Soc. 43 (2006), no. 3, 543-549   과학기술학회마을   DOI   ScienceOn
13 S. H. Sung, T. C. Hu, and A. I. Volodin, On the weak laws for arrays of random variables, Statist. Probab. Lett. 72 (2005), no. 4, 291-298   DOI   ScienceOn