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On the almost sure convergence for dependent random vectors in Hilbert spaces

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Abstract

This work develops almost sure convergence of negatively associated random vectors in Hilbert spaces. Extensions of a result in [4] are given. Illustrative examples are provided.

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References

  1. J. I. Baek and S. T. Park, Convergence of weighted sums for arrays of negatively dependent random variables and its applications, J. Theoret. Probab., 23 (2010), 362–377.

    Article  MathSciNet  MATH  Google Scholar 

  2. B. Y. Jing and H. Y. Liang, Strong limit theorems for weighted sums of negatively associated random variables, J. Theoret. Probab., 21 (2008), 890–909.

    Article  MathSciNet  MATH  Google Scholar 

  3. K. Joag-Dev and F. Proschan, Negative association of random variables, with applications, Ann. Statist., 11 (1983), 286–295.

    Article  MathSciNet  MATH  Google Scholar 

  4. M. H. Ko, T. S. Kim and K. H. Han, A note on the almost sure convergence for dependent random variables in a Hilbert space, J. Theoret. Probab., 22 (2009), 506–513.

    Article  MathSciNet  MATH  Google Scholar 

  5. S. Kochen and C. Stone, A note on the Borel–Cantelli lemma, Illinois J. Math., 8 (1964), 248–251.

    MathSciNet  MATH  Google Scholar 

  6. P. Matula, A note on the almost sure convergence of sums of negatively dependent random variables, Statist. Probab. Lett., 15 (1992), 209–213.

    Article  MathSciNet  MATH  Google Scholar 

  7. F. Móricz, Strong limit theorems for blockwise m-dependent and blockwise quasiorthogonal sequences of random variables, Proc. Amer. Math. Soc., 101 (1987), 709–715.

    Article  MathSciNet  MATH  Google Scholar 

  8. F. Móricz, U. Stadtmüller and M. Thalmaier, Strong laws for blockwise \({\mathcal{M}}\)-dependent random fields, J. Theoret. Probab., 21 (2008), 660–671.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Rosalsky and L. V. Thanh, On the strong law of large numbers for sequences of blockwise independent and blockwise p-orthogonal random elements in Rademacher type p Banach spaces, Probab. Math. Statist., 27 (2007), 205–222.

    MathSciNet  MATH  Google Scholar 

  10. U. Stadtmüller and L. V. Thanh, On the strong limit theorems for double arrays of blockwise M-dependent random variables, Acta Math. Sin. (Engl. Ser.), 27 (2011), 1923–1934.

    Article  MathSciNet  Google Scholar 

  11. L. V. Thanh, On the Brunk–Chung type strong law of large numbers for sequences of blockwise m-dependent random variables, Esaim: P&S., 10 (2006), 258–268.

    Article  MATH  Google Scholar 

  12. L. V. Thanh, On the strong law of large numbers for d-dimensional arrays of random variables, Electron. Comm. Probab., 12 (2007), 434–441.

    MathSciNet  MATH  Google Scholar 

  13. G. D. Xing and S. C. Yang, Some exponential inequalities for positively associated random variables and rates of convergence of the strong law of large numbers, J. Theoret. Probab., 23 (2010), 169–192.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. F. Wang and L. X. Zhang, A nonclassical law of the iterated logarithm for functions of positively associated random variables, Metrika, 64 (2006), 361–378.

    Article  MathSciNet  MATH  Google Scholar 

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Correspondence to Le Van Thanh.

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This work was supported by the Vietnam’s National Foundation for Science and Technology Development (NAFOSTED).

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Thanh, L.V. On the almost sure convergence for dependent random vectors in Hilbert spaces. Acta Math Hung 139, 276–285 (2013). https://doi.org/10.1007/s10474-012-0275-7

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  • DOI: https://doi.org/10.1007/s10474-012-0275-7

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