I.I.D.随机变量部分和之随机和的极限定理

Limit Theorems of Random Sum of Partial Sums on I.I.D. Random Variable

论文研究了部分和之随机和的大数律和中心极限定理 ,所得结果推广了文献[4 ]中部分和之和的大数律和中心极限定理 .此外 ,论文还研究了由部分和之和所定义的停时 。

In classical limit theory, the sum of i.i.d.(indep e ndent,identically,distributed) random variables is often considered. Because of the importance of random sum in finance and insurance, it is necessary to investiga te the case of random sums. This paper considers the sum of partial sums of i.i .d. random variables in the case of random sums. The weak law of large numbers(W LLN) and the central limit thorem (CLT) were established. The authors do not de mand that random index be independent of additive terms in our results. What is more, stopping time defined by the sum of partial sums was investigated and its asymptotic norma l behavior was also obtained. These results are not only significant general izations of classical ones but also promise useful applications.