On the Hartman–Wintner law of the iterated logarithm under sublinear expectation

Abstract

In this article, we establish two types of the Hartman–Wintner law of the iterated logarithm under sublinear expectations, especially for pseudo-independent random variables with the finite quadratic Choquet expectations, which generalizes the existing results for independent and identically distributed sequences. But unlike the classical situation, one counterexample is provided to show that the Hartman–Wintner law of the iterated logarithm may fail on the sublinear expectation space only with the finite second moment condition.