It is an interested problem when the inverse moments of nonnegative independent summation can be approximated by the inverse of moments of them. In the strong moments conditions, this problem is studied in the reference. Recently, WU, et. all. significantly improved these moment conditions, in this paper, the inverse moments are extended further to the summations of nonnegative NA random variables and nonnegative sub-martingale, and it is discussed when only the second moment exist. |