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Article

Son, Ta Cong ; Thang, Dang Hung ; Dung, Le Van
Complete convergence in mean for double arrays of random variables with values in Banach spaces. (English). Applications of Mathematics, vol. 59 (2014), issue 2, pp. 177-190
MSC: 60B11, 60B12, 60F15, 60F25 | MR 3183471 | Zbl 06362220 | DOI: 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
Summary:
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.
References:
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