Some Marshall Type Probability Inequalities For Demi(Sub)Martingales And Strong Law Of Large Numbers For Conditional Demi(sub)martingales

Demi(sub)martingale and conditional demi(sub)martingale are two types of de-pendent random variable sequences which are more extensive than martingale.If{Sn,n?1} is a demimartingale,g(·)is a nondecreasing convex function,then{g(Sn),n?1} is a demisubmartingale.Based on the existed the Marshall type probability inequalities for the demi-martingale sequence {Sn,n?1},we further explore the Marshall type probabil-ity inequality for demimartingale and demisubmartingale like {g(Sn),n?1} and{Sn,n?1} in this paper,in order to obtain the limit theorem for conditional demi(sub)martingale.The main works are as follows:Firstly,we give some maximum inequalities and minimum inequalities of Mar-shall type probability inequalities for demimartingale and demisubmartingale like{g(Sn),n? 1} and {Sn,n?1},some of these conclusions generalize and improve the corresponding results in recent papers.Secondly,we establish some Brunk-Prokhorov strong law of large numbers for conditional demimartingale and conditional demisubmartingale sequence {Sn,n?1}.