Study On Moment Inequalities For Several Classes Of Demimartingales And Their Applications

N-demimartingales and conditional demisubmartingales are two types sequences of dependent random variables which are more extensive than martingales sequences.In this paper,we obtain moment inequalities for several classes of "demimartingales" sequences by using the conditional Fubini theorem and the conditional Holder inequality,which are based on the existing maximal inequality for N-demimartingales.In addition,we give a class of Brunk-Prokhorov type strong law of large numbers for N-demimartingales.The main works of this paper are as follows:(1)A class of conditional moment inequalities for nonnegative conditional demimartingales is obtained using several elementary inequalities.(2)A class of minimal inequalities for nonnegative conditional demimartingales is given,and conditional moment inequalities for nonnegative conditional demimartingales are obtained.(3)A class of moment inequalities for N-demimartingales is established.On this basis,the Brunk-Prokhorov type strong law of large numbers for N-demimartingales is given.