Some Probability Inequalities For Demimartingales And Conditional Demimartingales

Demi(sub)martingale and conditional demi(sub)martingale are two types of de-pendent random variable sequences which are more extensive than martingale.Let{Sn,n ? 1} is a demimartingale,g(·)is a nondecreasing convex function,then{g(Sn),n?1} is a demisubmartingale.Based on the existed probability inequalities for the demimartingale sequence{Sn,n ?1},we explore the probability inequality of dependent random variable sequence for demimartingale and conditional demimartingale like {cnSn,n?1} and{cng(Sn),n?1} in this paper.Meanwhile,we give a class of minimal inequalities for conditional demi(sub)martingale.The main works are as follows:Firstly,we give some minimal inequalities of dependent sequence for demi-martingale and conditional demimartingale like {cnSn,n? 1} and {cng(Sn),n? 1},some of these results generalize and improve the corresponding results in recent pa-pers.Secondly,we establish some maximal inequalities for demisubmartingale se-quence {g(Sn),n ? 1}.