Some new results for weakly dependent random variable sequences. (English) Zbl 1240.60085

Summary: Let \(\{X_n,n\geq 1\}\) be a \(\widetilde{\rho}\)-mixing random variable sequence. By using the truncation method of random variables and the three series theorem for \(\widetilde{\rho}\)-mixing sequences, the convergence properties of \(\widetilde{\rho}\)-mixing sequence are discussed, and a class of strong limit theorems for \(\widetilde{\rho}\)-mixing sequences are obtained, which generalize the corresponding results for independent sequences. At last, the strong stability for weighted sums of \(\widetilde{\rho}\)-mixing sequences is studied.


60F15 Strong limit theorems