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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 49561, 15 pages
http://dx.doi.org/10.1155/JAMSA/2006/49561

Mean convergence theorems and weak laws of large numbers for double arrays of random variables

Department of Mathematics, Vinh University, Nghe An 42118, Vietnam

Received 26 June 2005; Revised 11 September 2005; Accepted 16 September 2005

Copyright © 2006 Le Van Thanh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Adler, A. Rosalsky, and R. L. Taylor, “A weak law for normed weighted sums of random elements in Rademacher type p Banach spaces,” Journal of Multivariate Analysis, vol. 37, no. 2, pp. 259–268, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. A. Adler, A. Rosalsky, and R. L. Taylor, “Some strong laws of large numbers for sums of random elements,” Bulletin of the Institute of Mathematics. Academia Sinica, vol. 20, no. 4, pp. 335–357, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. A. Bose and T. K. Chandra, “Cesàro uniform integrability and Lp convergence,” Sankhyā. Series A, vol. 51, pp. 12–28, 1993. View at Google Scholar · View at Zentralblatt MATH
  4. T. K. Chandra, “Uniform integrability in the Cesàro sense and the weak law of large numbers,” Sankhyā. Series A, vol. 51, no. 3, pp. 309–317, 1989. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. T. K. Chandra and A. Goswami, “Cesàro uniform integrability and the strong law of large numbers,” Sankhyā. Series A, vol. 54, no. 2, pp. 215–231, 1992. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Y. S. Chow and H. Teicher, Probability Theory. Independence, Interchangeability, Martingales, Springer Texts in Statistics, Springer, New York, 3rd edition, 1997. View at Zentralblatt MATH · View at MathSciNet
  7. A. Gut, “Marcinkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices,” Annals of Probability, vol. 6, no. 3, pp. 469–482, 1978. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. M. Ordóñez Cabrera, “Limit theorems for randomly weighted sums of random elements in normed linear spaces,” Journal of Multivariate Analysis, vol. 25, no. 1, pp. 139–145, 1988. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. M. Ordóñez Cabrera, “Convergence of weighted sums of random variables and uniform integrability concerning the weights,” Collectanea Mathematica, vol. 45, no. 2, pp. 121–132, 1994. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. Ordóñez Cabrera and A. I. Volodin, “Mean convergence theorems and weak laws of large numbers for weighted sums of random variables under a condition of weighted integrability,” Journal of Mathematical Analysis and Applications, vol. 305, no. 2, pp. 644–658, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. A. Rosalsky, M. Sreehari, and A. I. Volodin, “Mean convergence theorems with or without random indices for randomly weighted sums of random elements in Rademacher type p Banach spaces,” Stochastic Analysis and Applications, vol. 21, no. 5, pp. 1169–1187, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. L. Van Thanh, “On the Lp-convergence for multidimensional arrays of random variables,” International Journal of Mathematics and Mathematical Sciences, vol. 2005, no. 8, pp. 1317–1320, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  13. B. von Bahr and C.-G. Esseen, “Inequalities for the rth absolute moment of a sum of random variables, 1r2,” Annals of Mathematical Statistics, vol. 36, pp. 299–303, 1965. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. D. Wei and R. L. Taylor, “Convergence of weighted sums of tight random elements,” Journal of Multivariate Analysis, vol. 8, no. 2, pp. 282–294, 1978. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet