A new type of compact uniform integrability with application to degenerate mean convergence of weighted sums of Banach space valued random elements

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:487

Article

Cabrera, Manuel Ordonez¹  Rosalsky, Andrew²  Unver, Mehmet³  Volodin, Andrei⁴ 

[1] Univ Seville, Dept Math Anal, E-41080 Seville, Spain

[2] Univ Florida, Dept Stat, Gainesville, FL 32611 USA

[3] Ankara Univ, Fac Sci, Dept Math, TR-06100 Ankara, Turkey

[4] Univ Regina, Dept Math & Stat, Regina, SK S4S 0A2, Canada

关键词: Real separable Banach space;    Array of random elements;    Weighted sums;    Compact uniform integrability;    Mean convergence;   

DOI  :  10.1016/j.jmaa.2020.123975

来源: Elsevier

【 摘 要 】

In this correspondence, for an array {Xnk : un < k < E N} of integrable random elements in a real separable Banach space and an array {a,, : u < k < n E N} of real numbers, a new type of compact uniform integrability is introduced and it is used to obtain degenerate mean convergence theorems for the weighted V, sums E a k(X.,,,k n E N. More specifically, conditions are provided k=u under which lim E n-400 E a,,k(Xnk EX k) k=u, = 0. 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free