Geodesic
On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements
Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 533-547

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By applying a recent result of Hu et al. [Stochastic Anal. Appl., 17 (1999), pp. 963–992], we extend and generalize the complete convergence results of Pruitt [J. Math. Mech., 15 (1966), pp. 769–776] and Rohatgi [Proc. Cambridge Philos. Soc., 69 (1971), pp. 305–307] to arrays of row-wise independent Banach space valued random elements. No assumptions are made concerning the geometry of the underlying Banach space. Illustrative examples are provided comparing the various results.
Keywords: array of Banach space valued random elements, row-wise independence, weighted sums, complete convergence, rate of convergence, almost sure convergence. 
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     author = {T.-C. Hu and D. Li and A. Rosalsky and A. I. Volodin},
     title = {On the rate of complete convergence for weighted sums of arrays of {Banach} space valued random elements},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     volume = {47},
     number = {3},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a5/}
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T.-C. Hu; D. Li; A. Rosalsky; A. I. Volodin. On the rate of complete convergence for weighted sums of arrays of Banach space valued random elements. Teoriâ veroâtnostej i ee primeneniâ, Tome 47 (2002) no. 3, pp. 533-547. http://geodesic.mathdoc.fr/item/TVP_2002_47_3_a5/