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On convergence properties of sums of dependent random variables under second moment and covariance restrictions

Author

Listed:
  • Hu, Tien-Chung
  • Rosalsky, Andrew
  • Volodin, Andrei

Abstract

For a sequence of dependent square-integrable random variables and a sequence of positive constants {bn,n>=1}, conditions are provided under which the series converges almost surely as n-->[infinity] and {Xn,n>=1} obeys the strong law of large numbers almost surely. The hypotheses stipulate that two series converge, where the convergence of the first series involves the growth rates of and {bn,n>=1} and the convergence of the second series involves the growth rate of .

Suggested Citation

  • Hu, Tien-Chung & Rosalsky, Andrew & Volodin, Andrei, 2008. "On convergence properties of sums of dependent random variables under second moment and covariance restrictions," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 1999-2005, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:1999-2005
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    Cited by:

    1. Cousido-Rocha, Marta & de Uña-Álvarez, Jacobo & Hart, Jeffrey D., 2019. "A two-sample test for the equality of univariate marginal distributions for high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Prass, Taiane Schaedler & Pumi, Guilherme, 2021. "On the behavior of the DFA and DCCA in trend-stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    3. Guilherme Pumi & Taiane Schaedler Prass & Rafael Rigão Souza, 2021. "A dynamic model for double‐bounded time series with chaotic‐driven conditional averages," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 68-86, March.

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