Abstract
Let {Xn; n≥1} be a sequence of independent and identically distributed U[0, Citation1]-distributed random variables. Define the uniform empirical process , 0≤t≤1, and |Fn|=sup 0≤t≤1|Fn(t)|. This paper is concerned with a general case of the almost sure central limit theorem of |Fn| and sup 0≤t≤1Fn(t).
Acknowledgement
Thanks are due to professor Zhengyan Lin of Zhejiang University and Zuoxiang Peng of Southwest University in China for their help. This work is supported by the National Natural Science Foundation of China (grant 11326174), Natural Science Foundation of Jiangsu Province (grant BK20130412), Natural Science Research Project of Ordinary Universities in Jiangsu Province (grant 12KJB110003).