This article is cited in 22 papers

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

T.-C. Hu^a, D. Li^b, A. Rosalsky^c, A. I. Volodin<sup>d

a</sup> National Tsing Hua University, Department of Mathematics
^b Lakehead University
^c University of Florida
^d Kazan State University

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.

Keywords: array of Banach space valued random elements, row-wise independence, weighted sums, complete convergence, rate of convergence, almost sure convergence.

Received: 26.10.1999

Language: English

DOI: 10.4213/tvp3691

 English version: Theory of Probability and its Applications, 2003, 47:3, 455–468

Bibliographic databases:

• 
• 
•