Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications

• Published in: Acta mathematica Sinica. English series Vol. 35; no. 2; pp. 172 - 184
• Main Authors: Xu, Jia Pan, Zhang, Li Xin
• Format: Journal Article
• Language: English
• Published: Beijing Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.02.2019; Springer Nature B.V
• Subjects: Independent variables; Mathematics; Mathematics and Statistics; Random variables; Theorems; Sub-linear expectation; Marcinkiewicz’s strong law of large numbers; Kolmogorov’s three series theorem; Rosenthal’s inequality; capacity; 60F15

In this paper, motived by the notion of independent and identically distributed random variables under the sub-linear expectation initiated by Peng, we establish a three series theorem of independent random variables under the sub-linear expectations. As an application, we obtain the Marcinkiewicz’s...