Some Probability Inequalities And Their Applications For Conditional Demi(Sub) Martingales

Based on the limit theory of demimartingales and conditional demimartin-gales, some probability inequalities and limit theorems for conditional demi(sub)-martingales are studied in this thesis. Our main results are as follows:Firstly, we obtain some moment inequalities for nonnegative conditional demisub-martingales by using some elementary inequalities in the theory of real numbers and our results generalize the corresponding conclusions in [31].Secondly, we establish the Whittle inequalities for conditional demi(sub)martin-gales. In addition, we get another Hajck-Renyi inequality for conditional demi-martingales and conditional associated random variables.Thirdly, some limit theorems for conditional demi(sub)martingales are obtained by applying some inequalities established above.