155
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

L1-Convergence for Weighted Sums of Some Dependent Random Variables

, &
Pages 928-936 | Received 19 Oct 2009, Accepted 27 Jul 2010, Published online: 29 Oct 2010

References

  • Adler , A. , Rosalsky , A. , and Volodin , A. 1997 . A mean convergence theorem and weak law for arrays of random elements in martingale type p Banach spaces . Statist. Probab. Lett. 32 : 167 – 174 .
  • Bryc , W. , and Smolénski , W. 1993 . Moment conditions for almost sure convergence of weakly correlated random variables . Proceedings of the American Mathematical Society 119 ( 2 ): 629 – 635 .
  • Chen P.Y. , Liu J.J. , and Gan S.X. 1998 . Convergence for B-valued random fields and the type of Banach spaces. J. Wuhan Univ. (Natural Science Edition), 44(1):11–14. (in Chinese)
  • Ordóñez Cabrera , M. , and Volodin , A. 2005 . 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 305 : 644 – 658 .
  • Pyke , R. , and Root D. 1968 . On convergence in r-mean of normalized partial sums . Ann Math Statist. 39 : 379 – 381 .
  • Shao , Q.M. 1988 . A moment inequality and its applications . Acta Math. Sinica 31 : 736 – 747 . (in Chinese)
  • Shao , Q.M. 1995 . Maximal inequalities for partial sums of ρ-mixing sequences . Annals of Probability 23 : 948 – 965 .
  • Sung , S.H. , Lisawadi , S. , and Volodin , A. 2008 . Weak laws of large numbers for arrays under a condition of uniform integrability . Journal of the Korean Mathematical Society 45 : 289 – 300 .
  • Yang , S.-C. 1995 . Almost sure convergence of weighted sums of mixing sequences . Journal of Systems Science and Mathematical Sciences 15 : 254 – 265 . (in Chinese)

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.