On Strong Convergence for Weighted Sums of a Class of Random Variables

الملخص EN

Let {Xn,n≥1} be a sequence of random variables satisfying the Rosenthal-type maximal inequality.

Complete convergence is studied for linear statistics that are weighted sums of identically distributed random variables under a suitable moment condition.

As an application, the Marcinkiewicz-Zygmund-type strong law of large numbers is obtained.

Our result generalizes the corresponding one of Zhou et al.

(2011) and improves the corresponding one of Wang et al.

(2011, 2012).