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Complete convergence in mean for double arrays of random variables with values in Banach spaces

Applications of Mathematics volume 59, pages 177–190 (2014)Cite this article

Abstract

The rate of moment convergence of sample sums was investigated by Chow (1988) (in case of real-valued random variables). In 2006, Rosalsky et al. introduced and investigated this concept for case random variable with Banach-valued (called complete convergence in mean of order p). In this paper, we give some new results of complete convergence in mean of order p and its applications to strong laws of large numbers for double arrays of random variables taking values in Banach spaces.

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Authors and Affiliations

  1. Hanoi University of Science, Hanoi, Vietnam

    Ta Cong Son & Dang Hung Thang

  2. Da Nang University of Education, Da Nang, Vietnam

    Le Van Dung

Authors
  1. Ta Cong Son
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  2. Dang Hung Thang
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  3. Le Van Dung
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Correspondence to Ta Cong Son.

Additional information

The research of the first author (grant no. 101.03-2013.02), second author (grant no. 101.03-2013.02) and third author (grant no. 10103-2012.17) have been partially supported by Vietnams National Foundation for Science and Technology Development (NAFOSTED). The research of the first author has been partially supported by project TN-13-01.

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Son, T.C., Thang, D.H. & Dung, L.V. Complete convergence in mean for double arrays of random variables with values in Banach spaces. Appl Math 59, 177–190 (2014). https://doi.org/10.1007/s10492-014-0048-4

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  • DOI: https://doi.org/10.1007/s10492-014-0048-4

Keywords

  • complete convergence in mean
  • double array of random variables with values in Banach space
  • martingale difference double array
  • strong law of large numbers
  • p-uniformly smooth space

MSC 2010

  • 60B11
  • 60B12
  • 60F15
  • 60F25