Research article

The law of iterated logarithm for a class of random variables satisfying Rosenthal type inequality

  • Received: 06 June 2021 Accepted: 28 July 2021 Published: 02 August 2021
  • MSC : 60F05, 60F15

  • Let $ \{Y_n, n\geq 1\} $ be sequence of random variables with $ EY_n = 0 $ and $ \sup_nE|Y_n|^p < \infty $ for each $ p > 2 $ satisfying Rosenthal type inequality. In this paper, the law of the iterated logarithm for a class of random variable sequence with non-identical distributions is established by the Rosenthal type inequality and Berry-Esseen bounds. The results extend the known ones from i.i.d and NA cases to a class of random variable satisfying Rosenthal type inequality.

    Citation: Haichao Yu, Yong Zhang. The law of iterated logarithm for a class of random variables satisfying Rosenthal type inequality[J]. AIMS Mathematics, 2021, 6(10): 11076-11083. doi: 10.3934/math.2021642

    Related Papers:

  • Let $ \{Y_n, n\geq 1\} $ be sequence of random variables with $ EY_n = 0 $ and $ \sup_nE|Y_n|^p < \infty $ for each $ p > 2 $ satisfying Rosenthal type inequality. In this paper, the law of the iterated logarithm for a class of random variable sequence with non-identical distributions is established by the Rosenthal type inequality and Berry-Esseen bounds. The results extend the known ones from i.i.d and NA cases to a class of random variable satisfying Rosenthal type inequality.



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