Maximal Inequalities For The Partial Sum Of The Sequences For The Product Of The Associated Sequences And Their Applications

Let {Xn,n ? 1} be a sequence of Ll random variables,and let {Yn,n ? 1} be a sequence of nonnegative,independent random variables and independent of the Xi(i = 1,2,...).Let Tn =(?)is the partial sum of mean zero positively associated random variables,then {Tn,n ? 1} is a demimartingale.If {Xn,n ? 1} is the partial sum of mean zero conditional negatively associated random variables,then {Tn,n ? 1} is a conditional N-demimartingale.Based on relevant literatures,this thesis explores the probability inequalities that {Tn,n ? 1} satisfies when {Xn,n? 1} is the partial sum of mean zero positively associated random variables or when {Xn,n ? 1} is the partial sum of mean zero conditional negatively associated random variables combined with some elementary inequalities in the theory of real number.At the same time,the application of some inequalities is given.Our main results are as follows:Firstly,we obtain some maximal inequalities for the partial sum of the sequences for the product of the PA sequences by using some elementary inequalities.Secondly,we establish some maximal inequalities for the partial sums of se-quences of the product of the conditional NA sequences by using some special func-tions.Thirdly,some limit results and moment inequalities for {Tn,n?1} are ob-tained by applying some inequalities established above.