Precise asymptotics of moving average process under $phi$-mixing assumption

摘要

In the paper by Liu and Lin (Statist. Probab. Lett. 76 (2006), no. 16, 1787--1799), a new kind of precise asymptotics in the law of large numbers for the sequence of i.i.d. random variables, which includes complete convergence as a special case, was studied. This paper is devoted to the study of this new kind of precise asymptotics in the law of large numbers for moving average process under $phi$-mixing assumption and some results of Liu and Lin [6] are extended to such moving average process.