On the rate of complete convergence for weighted sums of arrays of banach space valued random elements

Abstract

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 Danach space valued random elements. No assumptions are made concerning the geometry of the underlying Banach space. Illustrative examples are provided comparing the various results.