Marcinkiewicz Type Strong Laws Of Large Number Under Nonlinear Expectation Space

The sub-linear expectation space is a nonlinear expectation space having advantages of modelling uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expecation to replace probability and expecation of classical probability theory. The sub-linear expec-tation has the property of nonlinearity, which could model uncertainty and reflect the real world better.In this paper, the method of selecting subsequence is used to prove Marcinkiewicz type strong laws of large numbers under sub-linear expec-tation space. This result is a natural extension of the classical Marcinkiewicz’s strong laws of large numbers to the case where the expectation is nonadditive. In addition, this paper also discusses the central limit theorem and laws of the iterated logarithm under sub-linear expectation space.