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Applications of Mathematics

, Volume 59, Issue 2, pp 177–190 | Cite as

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

  • Ta Cong SonEmail author
  • Dang Hung Thang
  • Le Van Dung
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.

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 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2014

Authors and Affiliations

  1. 1.Hanoi University of ScienceHanoiVietnam
  2. 2.Da Nang University of EducationDa NangVietnam

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