Skip to main content
SpringerLink
Log in

On the strong law of large numbers for sequences of dependent random variables

  • Mathematics
  • Published:
Vestnik St. Petersburg University: Mathematics Aims and scope Submit manuscript

Abstract

New sufficient conditions for the applicability of the strong law of large numbers are established for sequences of random variables without the independence conditions. Results on strong stability of sums of dependent random variables are also obtained. No particular type of dependence between random variables of a sequence is assumed. Only conditions related to moments of random variables and their sums are used. It is shown that the results obtained are unimprovable in certain sense. These results are generalizations of some results of N. Etemadi proved under more restrictive conditions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. V. Petrov and V. M. Korchevsky. “On the Strong Law of Large Numbers for Sequences of Dependent Random Variables,” Proceedings of the 6th St. Petersburg Workshop on Simulation, 977–980 (2009).

  2. V. V. Petrov, “On the Strong Law of Large Numbers for Sequences of Non-negative Random Variables,” Teor. veroyatn. i primen. 53(2), 379–382 (2008).

    Google Scholar 

  3. V. V. Petrov, “On the Stability of Sums of Non-negative Random Variables,” Zapiski nauchn. sem. POMI 361, 78–82 (2008).

    Google Scholar 

  4. N. Etemadi, “On the Law of Large Numbers for Non-negative Random Variables,” J. Multivariate Analysis 13, 187–193 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  5. N. Etemadi, “Stability of Sums of Weighted Non-negative Random Variables,” J. Multivariate Analysis 13, 361–365 (1983).

    Article  MATH  MathSciNet  Google Scholar 

  6. V. V. Petrov, Sums of Independent Random Variables (Nauka, Moscow, 1972; Springer, New York, 1975).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    V. M. Korchevsky & V. V. Petrov

Authors
  1. V. M. Korchevsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. V. Petrov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. M. Korchevsky.

Additional information

Original Russian Text © V.M. Korchevsky, V.V. Petrov, 2010, published in Vestnik Sankt-Peterburgskogo Universiteta. Seriya 1. Matematika, Mekhanika, Astronomiya, 2010, No. 3, pp. 26–30.

About this article

Cite this article

Korchevsky, V.M., Petrov, V.V. On the strong law of large numbers for sequences of dependent random variables. Vestnik St.Petersb. Univ.Math. 43, 143–147 (2010). https://doi.org/10.3103/S1063454110030040

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1063454110030040

Keywords

Search

Navigation