Geodesic
A~note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elements
Lobachevskii journal of mathematics, Tome 15 (2004), pp. 21-33

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We obtain complete convergence results for arrays of rowwise independent Banach space valued random elements. In the main result no assumptions are made concerning the geometry of the underlying Banach space. As corollaries we obtain results on complete convergence in stable type $p$ Banach spaces.
Keywords: array of Banach space valued random elements, stable type $p$ Banach space, rowwise independence, weighted sums, complete convergence, rate of convergence, almost sure convergence, convergence in probability. 
@article{LJM_2004_15_a2,
     author = {A. I. Volodin and R. Antonini and T.-Ch. Hu},
     title = {A~note on the rate of complete convergence for weighted sums of arrays of {Banach} space valued random elements},
     journal = {Lobachevskii journal of mathematics},
     pages = {21--33},
     publisher = {mathdoc},
     volume = {15},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2004_15_a2/}
}
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A. I. Volodin; R. Antonini; T.-Ch. Hu. A~note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elements. Lobachevskii journal of mathematics, Tome 15 (2004), pp. 21-33. http://geodesic.mathdoc.fr/item/LJM_2004_15_a2/