Equivalent Conditions of Complete Moment Convergence ofWeighted Sums for phi- Mixing Sequence of Random Variables

摘要

In this article, the complete moment convergence of weighted sums for phi-mixing sequence of random variables is investigated. By applying moment inequality and truncation methods, the equivalent conditions of complete moment convergence of weighted sums for phi-mixing sequence of random variables are established. These results promote and improve the corresponding results obtained by Li etal. (1995) and Gut (1993) from i.i.d. to phi-mixing setting. Moreover, we obtain the complete moment convergence of moving average processes based on phi-mixing random variables, which extends the result of Kim etal. (2008) in the sense that it does not require a specific mixing rate.