In this paper we investigate stopped partial sums for weak dependent sequences. In particular, the results are used to obtain new maximal inequalities for strongly mixing sequences and related almost sure results.
Magda Peligrad. "Convergence of Stopped Sums of Weakly Dependent Random Variables." Electron. J. Probab. 4 1 - 13, 1999. https://doi.org/10.1214/EJP.v4-50