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Weak Law of Large Numbers Without Any Restriction on the Dependence Structure of Random Variables

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Abstract

In this paper, we prove that weak law of large numbers for stochastically dominated random variables without any restriction on the dependence structure.

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References

  1. Adler, A., Rosalsky, A.: Some general strong laws for weighted sums of stochastically dominated random variables. Stoch. Anal. Appl. 5(1), 1–16 (1987)

    Article  MathSciNet  Google Scholar 

  2. Bingham, N.H., Goldie, C.M., Teugels, J.L.: Regular Variation. Cambridge University Press, Cambridge (1987)

    Book  Google Scholar 

  3. Boukhari, F.: Weak law of large numbers for maximal weighted sums of random variables. Commun. Statist. Theory Methods (2019). https://doi.org/10.1080/03610926.2019.1630437

    Article  MathSciNet  MATH  Google Scholar 

  4. Gut, A.: Probability: A Graduate Course. Springer, Berlin (2005)

    MATH  Google Scholar 

  5. Gut. A. 2004. An extension of the Kolmogorov-Feller weak law of large numbers with an application to the St. Petersburg Game. J. Theor. Probab. 17(3), 769–779

  6. Hall, P., Heyde, C.C.: Martingale Limit Theory and Its Application. Academic Press, Cambridge (1980)

    MATH  Google Scholar 

  7. Klesov, O.: Limit Theorems for Multi-Indexed Sums of Random Variables. Springer, Berlin (2014)

    Book  Google Scholar 

  8. Kruglov. V. M. 2011. A generalization of weak law of large numbers. Stoch. Anal. Appl. 29, 674–683

  9. Naderi, H., Boukhari, F., Matuła, P.: A note on the weak law of large numbers for weighted negatively superadditive dependent random variables. Commun. Statist. Theory Methods (2021). https://doi.org/10.1080/03610926.2021.1873377

    Article  Google Scholar 

  10. Naderi, H., Matuła, P., Amini, A., Ahmadzade, A.: A version of the Kolmogorov-Feller weak law of large numbers for maximal weighted sums of random variables. Commun. Statist. Theory Methods 48(21), 5414–5418 (2019)

    Article  Google Scholar 

  11. Naderi, H., Salehi, S.M., Matuła, P., Amini, A.: On weak law of large numbers for sums of negatively superadditive dependent random variables. Comptes Rendus Mathématique 375(1), 13–21 (2020)

    Article  MathSciNet  Google Scholar 

  12. Petrov, V.V.: Limit theorems of probability theory. Sequences of independent random variables. Clarendon Press, Oxford (1995)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran

    Habib Naderi

  2. Institute of Mathematics, Marie Curie-Skłodowska University, pl. M.C.-Skłodowskiej 1, 20-031, Lublin, Poland

    Przemysław Matuła

  3. Department of Statistics, Ordered Data, Reliability and Dependency Center of Excellence, Ferdowsi University of Mashhad, P.O. Box 91775-1159, Mashhad, Iran

    Mohammad Amini

Authors
  1. Habib Naderi
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  2. Przemysław Matuła
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  3. Mohammad Amini
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Correspondence to Habib Naderi.

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Communicated by Ahmad Parsian.

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Naderi, H., Matuła, P. & Amini, M. Weak Law of Large Numbers Without Any Restriction on the Dependence Structure of Random Variables. Bull. Iran. Math. Soc. 48, 1959–1965 (2022). https://doi.org/10.1007/s41980-021-00631-6

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  • DOI: https://doi.org/10.1007/s41980-021-00631-6

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