Chung型强大数定律及其应用

Chung Type Strong Laws of Large Numbers and Applications

利用逐项积分对Chung型强大数定律进行简单化证明,证明既不需要鞅收敛定理,也不需要三级数定理.应用Chung型强律,得到了随机序列的若于强大数定律和收敛速度等,这些定理和推论推广了Cantrell-Rosalsky强大数定律以及由Freedman(1974)建立的关于收敛速度的结果.这些结果除矩条件外,对随机变量的独立性和联合分布不作任何要求.

In this paper, a simplified proof of Chung type strong law of large numbers has been established. And in the proof, neither the martingale convergence theorem nor the three series theorem is used. As applying of Chung type strong laws, some strong laws of large numbers and convergence rates for arbitrary stochastic adapted sequences have been obtained~ These theorems and corollaries have extended the strong laws of large numbers es- tablished by Cantrell and Rosalsky and the convergence results obtained by Freedman（1974） For random sequences valuing on some point-set,the relationships of frequency and tran- sition probability have been established. In all the paper, no condition of independence or on the distribution of random variables are required except the conditions on moments of random variables.