Strong laws of large numbers for arrays of rowwise conditionally independent random elements. (1993) - Patterson Patterson, Ronald Frank Ronald Frank; Bozorgnia Bozorgnia, Abolghassem Abolghassem; Taylor Taylor, Robert Lee Robert Lee
Abstract : Let { X n k } be an array of rowwise conditionally independent random elements in a separable Banach space of type p, 1 ≤ p ≤ 2 . Complete convergence of n − 1 r ∑ k = 1 n X n k 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.