A probability inequality for sums of independent Banach space valued random variables. Issue 2 (17th February 2018)

• Record Type: Journal Article
• Authors: Li, Deli; Liang, Han-Ying; Rosalsky, Andrew
• Is Part Of: Stochastics. Volume 90:Issue 2(2018)
• Page Start: 214
• Page End: 223
• Publication Date: 2018-02-17
• Subjects: Probability inequality -- sums of independent Banach space valued random variables -- weak law of large numbers; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2017.1318878
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : Let be a real separable Banach space. Let and be two continuous and increasing functions defined on such that, , and is a nondecreasing function on . Let be a sequence of independent and symmetricB -valued random variables. In this note, we establish a probability inequality for sums of independentB -valued random variables by showing that for every and all, where and, . As an application of this inequality, we establish what we call a comparison theorem for the weak law of large numbers for independent and identically distributed -valued random variables.