Another form of Chover’s law of the iterated logarithm under sub-linear expectations

Abstract

In this paper, the Chover’s law of the iterated logarithm is established for a sequence of independent and identically distributed random variables under a sub-linear expectation space. As applications, several results on the Chover’s law of the iterated logarithm for traditional probability space have been generalized to the sub-linear expectation space context. Our results generalize those on Chover’s law of the iterated logarithm previously obtained by Qi and Cheng (Chinese Ann Math 17(A):195–206, 1996), Wu and Jiang (J Korean Stat Soc 39(2):199–206, 2010), and Wu (Acta Math Appl Sin (English Series) 32(2):385–394, 2016) from traditional probability space to the general sub-linear expectation space. There is no report on this form of Chover’s law of the iterated logarithm under sub-linear expectation, and we provide a method to study this subject.