The Asymptotic Distributions Of Sums And The Almost Sure Central Limit Theorem For The Product Of Parttial Sums

The Probability Theory is not only to improve the development of the theory of probability and mathematical statistics,but also is one of the main branches of the probability theory. Kolmogrov,one of famous former Soviet Union probability statistician,said:The Value of the probability theory is only to be revealed by the Limit Theorem, it is impossible to understand the real meaning of the basic probability theory without Limit Theorem. The probability theory are increasingly attention has been paid,it is widely used in aerospace, archaeological research, electronic technology,census and education,its methods and results will continue to improve and derivatives,and will have a huge impact on mathematical statistics and other disciplines. The CLT,to be importance of the basis theoretical of the theory of probability, will also continue to promote and applications.In1988,Brosamler and Schatte first proposed ASCLT under the i.i.d. Random variable sequence,Berkes,Multa,Shao qi-man and many other studiers had put theirs heart deeply in the ASCLT. Wang li,Wu qun-yin had studied The Asymptotic Distributions for products of the part Sums of the random variable sequence. Hu Xing,Song jia-yue,Xu qing-zhou,Zou hai-lian,Zhang li-xin and so on had studied The ASCLT for the product of partial sums of the random variable sequence. Based on the previous results,the paper does some improvement and promotion, and get some new results.First of all, in the first chapter,it gives the problem of this paper,the purpose and significance of the reserach topic. In addition,the research status and analysis.In the second place, it gives some background of the central limit theorem and the classical central limit theorem in several forms and advantages,its ideas and methods had a huge impact on us.In the third place, it gives the Asymptotic Distributions for products of the part Sums of the random variable sequence, and the paper get some new results.Finally, it discuss the ASCLT for the product of partial sums. On the babis of the third chapter,it docs the research of the ASCLT,and gets a new rusult.