Sequence Of Random Variables Limit Theorem

Probability limit theorem is not only the main branch of probability theory, but also is the basis and tool in other fields of probability theory and mathematical statistics.Multiple parameter limit theorem is extensively applied to biological information science, econometrics, and financial economics. Its methods and results continue to have great influence on other fields. So multiple parameter limit theorem is main research subject.Many mathematicians have generalized some results of one-parameter limit theorem to that of multiple parameter. In our country, Ling Zheng yan, Su Chun, Bai Zhi dong and Su Zhong gen have contributed to it. I do some work on the basis of their study.This paper includes five chapers. The first chaper introduces background of limit theorem of random variable. The second introduces law of large number, concept and theorem of convergence, and relationship in all kind of convergence, inequality in probability. The third discusses the strong law of large numbers for double arrays of pair-wise independent random variables. The fouth discusses the limit theorem of pairwise NQD sequences. It generalizes classical results of independent random variables.The last summarizes the main results.