Bahr-Esseen Type Moment Inequalities And Applications

In almost all branches of the mathematical sciences,the inequality often plays a vital role as well as in the probability limit.In relevant papers and books,some basic probability inequalities occur and be used frequently, so select or create a valid inequality is often a key step in solving the problem.At present,the conclusions of different types of random variable sequence and the theory and application combined with inequality have been elaborated many books, especially with regard to independent random Limit Theory variable has been maturing,and get a lot of deep results,more and more scholars began to study the case of non-independent,such as between two mutually independent random variables,pairwise NQD sequences, NA sequence,mixing sequences and the like have been get the relevant conclusions.While the Bahr-Esseen type moment inequality has good properties and applications in probability theory and mathematical statistics,so the paper try to get a more general result based on the results of existing research on Bahr-Esseen type moment inequalities.In this paper, firstly, censored integral approach combining Markov inequality was used to prove Bahr-Esseen type moment inequalities in the general case, then discussed the convergence of the general average of random variable sequence on the above inequality theoretical basis,finally,researched the Strong Law of the φ-mixing sequences and he existent problems of maximum value function of moment of t.