Some Probability Inequalities For Conditional N-demimartingales Based On Y Functions And Related Limit Results

Demimartingales,conditional demimartingales,N-demimartingales and condi-tional N-demimartingales are four types of random variables which are wider than martingales.Studying its probability inequalities have great significance to further explore their limit theorems.PA sequence is a kind of dependent random vari-ables,and the partial sum sequence of PA sequence with mean zero is a demi-martingale.Based on the probability inequalities for demimartingales and conditional demi-martingales,some maximal inequalities for demimartingales,conditional demimartin-gales,conditional N-demimartingales are obtained.Meanwhile a strong law of large numbers for PA sequences is also given in this thesis.Our main results are as follows:Firstly,we give another form of maximal inequalities for demimartingales and conditional demimartingales.Secondly,we establish maximal(?)-inequalities for conditional N-demimartingales based on Y functions,which makes related maximal inequalities for conditional demimartingales be generalized to the occasion of conditional N-demimartingales.Thirdly,H-R type inequality for PA sequences and a strong law of large numbers are obtained,which improves some related results in literature[36]and[37].