Complete convergence theorems for weighted row sums from arrays of random elements in Rademacher type p and martingale type p Banach spaces. Issue 6 (2nd November 2019)

• Record Type: Journal Article
• Authors: Hu, Tien-Chung; Rosalsky, Andrew; Volodin, Andrei
• Is Part Of: Stochastic analysis and applications. Volume 37:Issue 6(2019)
• Page Start: 1092
• Page End: 1106
• Publication Date: 2019-11-02
• Subjects: Complete convergence -- array of Banach space valued random elements -- weighted row sums -- Rademacher type p Banach space -- martingale type p Banach space -- rowwise independent -- martingale differences; Primary 60F15 -- 60B12 -- Secondary 60B11; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2019.1641414
• Languages: English
• ISSNs: 0736-2994

Abstract

Abstract: In this correspondence, complete convergence theorems are established for weighted row sums { ∑ i = 1 j a n, i V n, i, 1 ≤ j ≤ k n, n ≥ 1 } from arrays { V n, i, 1 ≤ i ≤ k n, n ≥ 1, k n → ∞ } of random elements taking values in real separable Rademacher type p ( 1 ≤ p ≤ 2 ) Banach spaces as well as real separable martingale type p ( 1 ≤ p ≤ 2 ) Banach spaces. It is assumed that sup { E ‖ V n, i ‖ p : 1 ≤ i ≤ k n, n ≥ 1 } < ∞ . A version of the Rademacher type p complete convergence theorem is also established with random variable weights. Illustrative examples are included.