Strong law of large numbers and Chover's law of the iterated logarithm under sub-linear expectations

Abstract

Limit theorems for sub-linear expectations are challenging field which have raised a large number of issues of interest recently. The aim of this paper is to establish general strong law of large numbers and the Chover's law of the iterated logarithm for a sequence of random variables under a sub-linear expectation space. As applications, several results on strong laws of large numbers which contain Marcinkiewicz strong law of large numbers and the Chover's law of the iterated logarithm for extended independence and identically distributed random variables have been generalized to the sub-linear expectation space context. Our results of strong laws of large numbers are more general than some related results previously reported obtained by Zhang (2016) [23], Cheng (2016) [5], Liu et al. (2015) [10] and Chen (2016) [3]. There is no report on the Chover's law of the iterated logarithm under sub-linear expectation, and we provide a method to study this subject.