Strong convergence of ρ˜-mixing random sequences.

The strong limit theory is one of the most important problems in the probability theory. Some results on the convergence of ρ ˜ -mixing random sequences have been presented. In this paper, we study the almost sure convergence for ρ ˜ -mixing random sequences. As a result, we generalize partial results of Wu and Jiang [Wu, Q. Y., and Y. Y. Jiang. 2008. Some strong limit theorems for q ˜ -mixing sequences of random variables. Statistics & Probability Letters 78:1017–23.]. We obtain the mainstream and some corresponding conclusions by using truncation methods and the generalized three-series theorem. A known result is generalized in this paper. [ABSTRACT FROM AUTHOR]