Strong convergence of ρ˜-mixing random sequences

Abstract

The strong limit theory is one of the most important problems in the probability theory. Some results on the convergence of $\tilde{\rho }$-mixing random sequences have been presented. In this paper, we study the almost sure convergence for $\tilde{\rho }$-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 $\tilde{q}$-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.

Keywords:

• $\tilde{\rho }$-mixing random sequences
• strong convergence theorem
• generalized three-series theorem

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (11571142).