Some Kinds Of The γ-type Probability Inequalities Of Two-Parameter Demimartingale And Strong Law Of Large Number

Demi(sub)martingale and conditional demi(sub)martingale are two types of dependent 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.This conculution is also true for two-parameter demi(sub)martingale and for two-parameter conditional demi(sub)martingale.Based on the existed the γ type probability inequalities for the demimartingale sequence {Sn,n≥)1},we further explore the γ type probability inequality for two-parameter demi(sub)martingale and two-parameter conditional demi(sub)martingale like {g(Sn),n≥1} and {Sn,n≥1} in this paper.Meanwhile we give the strong law of large number for two-parameter martingale differences.The main works are as follows:Firstly,we obtain a strong law of large number for conditional demi(sub)martingale.Secondly,we establish the γ type probability inequalities for two-parameter demi(sub)martingale and a strong law of large number for two-parameter martingale differences.Thirdly,we establish γ type probability inequalities for two-parameter conditional demi(sub)martingale.