Advertisement

Journal of Mathematical Sciences

, Volume 244, Issue 5, pp 805–810 | Cite as

On the Strong Law of Large Numbers for Sequences of Pairwise Independent Random Variables

  • V. M. KorchevskyEmail author
Article
  • 1 Downloads

We establish new sufficient conditions for the applicability of the strong law of large numbers (SLLN) for sequences of pairwise independent, nonidentically distributed random variables. These results generalize Etemadi’s extension of Kolmogorov’s SLLN for identically distributed random variables. Some of the obtained results hold with an arbitrary norming sequence in place of the classical normalization.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. Etemadi, “An elementary proof of the strong law of large numbers,” Z. Wahrsch. Verw. Gebiete, 55, 119–122 (1981).MathSciNetCrossRefGoogle Scholar
  2. 2.
    P. Matula, “A note on the almost sure convergence of sums of negatively dependent random variables,” Statist. Probab. Lett., 15, 209–213 (1992).MathSciNetCrossRefGoogle Scholar
  3. 3.
    P. Matula, “On some families of AQSI random variables and related strong law of large numbers,” Appl. Math. E-Notes, 5, 31–35 (2005).MathSciNetzbMATHGoogle Scholar
  4. 4.
    T. K. Chandra and A. Goswami, “Cesáro uniform integrability and a strong law of large numbers,” Sankhyā, Ser. A., 54, 215–231 (1992).MathSciNetzbMATHGoogle Scholar
  5. 5.
    A. Bose and T. K. Chandra, “A note on the strong law of large numbers,” Calcutta Statist. Assoc. Bull., 44, 115–122 (1994).MathSciNetCrossRefGoogle Scholar
  6. 6.
    V. M. Kruglov, “Strong law of large numbers,” in: V. M. Zolotarev, V. M. Kruglov, and V. Yu. Korolev (eds.), Stability Problems for Stochastic Models, TVP/VSP, Moscow–Utrecht, (1994), pp. 139–150.Google Scholar
  7. 7.
    V. A. Egorov, “A generalization of the Hartman–Wintner theorem on the law of the iterated logarithm,” Vesnt. Leningr. Univ., 7, 22–28 (1971).MathSciNetGoogle Scholar
  8. 8.
    V. V. Petrov, Sums of Independent Random Variables [in Russian], Moscow (1972).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2020

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

Personalised recommendations