Some New Results for Weakly Dependent Random Variable Sequences

Let $\{X_n,n\geq1\}$ be a $\wt{\rho}$-mixing random variable sequence. By using the truncation method of random variables and three series theorem of $\wt{\rho}$-mixing sequence, the convergence properties of $\wt{\rho}$-mixing sequence are discussed, and a class of strong limit theorems for $\wt{\rho}$-mixing sequence are obtained, which generalize the corresponding results of independent sequence. At last, the strong stability for weighted sums of $\wt{\rho}$-mixing sequence is studied