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 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.