Journal of Applied Mathematics and Stochastic Analysis 
Volume 6 (1993), Issue 1, Pages 1-9
doi:10.1155/S1048953393000012

Strong laws of large numbers for arrays of rowwise conditionally independent random elements

Ronald Frank Patterson,1 Abolghassem Bozorgnia,2 and Robert Lee Taylor3

 1Georgia State University, Department of Mathematics and Computer Science, Atlanta 30303, GA, USA
2Mashhad University, Department of Statistics, Mashhad, Iran
3University of Georgia, Department of Statistics, Athens 30602, GA, USA
Received 1 August 1992; Revised 1 January 1993

Abstract

Let {Xnk} be an array of rowwise conditionally independent random elements in a separable Banach space of type p, 1≤p≤2. Complete convergence of n−1r∑k=1nXnk to 0, 0<r<p≤2 is obtained by using various conditions on the moments and conditional means. A Chung type strong law of large numbers is also obtained under suitable moment conditions on the conditional means.