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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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
- 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