Strong laws of large numbers for arrays of rowwise conditionally independent random elements. (1993)

• Record Type: Journal Article
• Authors: Patterson Patterson, Ronald Frank Ronald Frank; Bozorgnia Bozorgnia, Abolghassem Abolghassem; Taylor Taylor, Robert Lee Robert Lee
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 6:Number 1(1993)
• Page Start: 1
• Page End: 9
• Publication Date: 1993
• Subjects: strong law of large numbers -- type p -- rowwise conditionally independent -- complete convergence; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953393000012
• Languages: English
• ISSNs: 1048-9533

Abstract

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.