Some Probability Inequalities Of Two-Parameter Demimartingales And Their Strong Law Of Large Numbers

As a generalization of the general sequence of random variables,the twoparameter demimartingale is a more extensive class of the sequence of dependent random variables than the demimartingale.In exploring the probabilistic properties of two-prarmeter demimartingales,the probability inequalities about two-parameter demimartingales and their strong law of large numbers are an indispensable part of the research process.In this thesis,on the basis of some probability inequalities of associated random variables and demimartingales,we obtain several classes of different probability inequalities about two-parameter demimartingales.Meanwhile,the convergence properties and the strong law of large numbers are given by related probability inequaliies.The main works are as follows:Firstly,we give a class of minimal inequality for two-parameter demimartingales by using the minimal inequalities of demimartingales.Secondly,we give the Marshall type inequalities for two-parameter demimartingales by using the Holder inequalities and a class of Chow type inequality.Thirdly,we give a moment inequality for two-parameter associated random variables and obtain the integrability of supremum and strong law of large numbers for that.At the same time,we give a Doob’s probability inequality and the BrunkProkhorov strong law of large numbers for two-parameter demimartingales.