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

摘要

In this paper, motived by the notion of independent and identicallydistributed random variables under the sub-linear expectation initiated byPeng, we give a theorem about the convergence of a random series and establisha three series theorem of independent random variables under the sub-linearexpectations. As an application, we obtain the Marcinkiewicz's strong law oflarge numbers for independent and identically distributed random variablesunder the sub-linear expectations. The technical details are different fromthose for classical theorems because the sub-linear expectation and its relatedcapacity are not additive.