Three Series Theorem for Independent Random Variables under Sub-linear Expectations with Applications - Xu, Jia Pan; Zhang, Li Xin (Acta mathematica Sinica. English series, 2019)
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 strong law of large numbers for independent and identically distributed random variables under the sub-linear expectations. The technical details are different from those for classical theorems because the sub-linear expectation and its related capacity are not additive.