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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.

##### MSC:
 60F15 Strong limit theorems