A General Law of Precise Asymptotics for the Complete Moment Convergence

The authors achieve a general law of precise asymptotics for a new kind of complete moment convergence of I.I.d,random variables,which includes complete con-vergence as a special case.It can describe the relations among the boundary function,weighted function,convergence rate and limit value in studies of complete convergence.This extends and generalizes the corresponding results of Liu and Lin in 2006.