Study On Inequality And Convergence Under Sublinear Expectations

This paper mainly discusses inequalities and some convergences of random vari-able sequence under sublinear expectations. Firstly we give several inequalities under sublinear expectation in contrast with classical probabilities, mainly including Markov inequality, Chebyshev inequality, Kolmogorov inequality, martingale inequality, and the use of these inequalities to prove the convergences of independent random variable sequences. Secondly we give several kinds of convergences of random variable sequences, including quasi surely convergence, quasi uniformly convergence, convergence in capacity and the relationships between these convergences. Finally we discuss the law of large numbers, central limit theorems and give some new results.