Some Limiting Properties Of Pairwise Independent Random Variables

With the gradually improve of independent random variables, more and more scholars begin to study the case of non-independent. As one of the common form of non-independent, the research of pairwise independent random variables has very important theory and actual significance. Kolmogorov and Gnedenko, famous statistician of former Soviet Union, once said: “The value of the cognitive theory of the probability can be revealed only through the theory of limit, if there is no limit theory of probability, we can’t throughly understand the basic concepts of probability theory.” Firstly, this paper obtains the r-th(1 ?r ?2)von Bahr-Esseen moment inequality use the method of truncation under integral combining Markov inequality. Secondly, ues the above inequality as the theoretical basis, this paper discusses the mean convergence of sequence of pairwise independent random variables. Finally, under the special circumstance, p ?1, 1 ?r ?2, we obtain the Baum- Katz type complete convergence of maximum partial sum of pairwise independent random, meanwhile, the conclusion are also extended to the field of pairwise independent random elements.