A strong law of large numbers for independent random variables under non-additive probabilities. Issue 21 (1st November 2020)

• Record Type: Journal Article
• Authors: Zhang, Ning; Lan, Yuting
• Is Part Of: Communications in statistics. Volume 49:Issue 21(2020)
• Page Start: 5252
• Page End: 5272
• Publication Date: 2020-11-01
• Subjects: Independent random variables -- non‐additive probabilities -- strong laws of large numbers -- upper expectations -- weak laws of large numbers; 60F15; 60F05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2019.1615508
• Languages: English
• ISSNs: 0361-0926

Abstract

Abstract: Under non‐additive probabilities, cluster points of the empirical average have been proved to quasi-surely fall into the interval constructed by either the lower and upper expectations or the lower and upper Choquet expectations. In this paper, based on the initiated notion of independence, we obtain a different Marcinkiewicz-Zygmund type strong law of large numbers. Then the Kolmogorov type strong law of large numbers can be derived from it directly, stating that the closed interval between the lower and upper expectations is the smallest one that covers cluster points of the empirical average quasi-surely.