Table of Contents Author Guidelines Submit a Manuscript
Discrete Dynamics in Nature and Society
Volume 2008, Article ID 140548, 10 pages
http://dx.doi.org/10.1155/2008/140548
Research Article

On Chung-Teicher Type Strong Law of Large Numbers for 𝜌 -Mixing Random Variables

Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38 D, 20-618 Lublin, Poland

Received 23 December 2007; Revised 5 March 2008; Accepted 20 March 2008

Academic Editor: Stevo Stevic

Copyright © 2008 Anna Kuczmaszewska. 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. R. C. Bradley, “On the spectral density and asymptotic normality of weakly dependent random fields,” Journal of Theoretical Probability, vol. 5, no. 2, pp. 355–373, 1992. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. W. Bryc and W. Smoleński, “Moment conditions for almost sure convergence of weakly correlated random variables,” Proceedings of the American Mathematical Society, vol. 119, no. 2, pp. 629–635, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. M. Peligrad, “Maximum of partial sums and an invariance principle for a class of weak dependent random variables,” Proceedings of the American Mathematical Society, vol. 126, no. 4, pp. 1181–1189, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. M. Peligrad and A. Gut, “Almost-sure results for a class of dependent random variables,” Journal of Theoretical Probability, vol. 12, no. 1, pp. 87–104, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. S. Utev and M. Peligrad, “Maximal inequalities and an invariance principle for a class of weakly dependent random variables,” Journal of Theoretical Probability, vol. 16, no. 1, pp. 101–115, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G.-H. Cai, “Strong law of large numbers for ρ-mixing sequences with different distributions,” Discrete Dynamics in Nature and Society, vol. 2006, Article ID 27648, 7 pages pages, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. M.-H. Zhu, “Strong laws of large numbers for arrays of rowwise ρ-mixing random variables,” Discrete Dynamics in Nature and Society, vol. 2007, Article ID 74296, 6 pages pages, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  8. I. Fazekas and O. Klesov, “A general approach to the strong laws of large numbers,” Theory of Probability and Its Applications, vol. 45, no. 3, pp. 436–449, 2000. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. K.-L. Chung, “Note on some strong laws of large numbers,” American Journal of Mathematics, vol. 69, no. 1, pp. 189–192, 1947. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. H. Teicher, “Some new conditions for the strong law,” Proceedings of the National Academy of Sciences of the United States of America, vol. 59, no. 3, pp. 705–707, 1968. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. I. Fazekas and T. Tómács, “Strong laws of large numbers for pairwise independent random variables with multidimensional indices,” Publicationes Mathematicae Debrecen, vol. 53, no. 1-2, pp. 149–161, 1998. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet