Yang Shan-chao

Moment inequalities for the partial sums of random variables

In this paper the usual Z 2 graded Lie algebra is generalized to a new form, which may be called Z 2,2 graded Lie algebra. It is shown that there exists close connections between the Z 2,2 graded Lie algebra and parastatistics, so the Z 2,2 can be used to study and analyse various symmetries and supersymmetries of the paraparticle systems.This paper discusses the conditions under which Rosenthal type inequality is obtained from M-Z-B type inequality. And M-Z-B type inequality is proved for a wide class of random variables. Hence Rosenthal type inequalities for some classes of random variables are obtained.