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Strong convergence properties and strong stability for weighted sums of AANA random variables. (English) Zbl 1321.60056

Summary: The Khintchine-Kolmogorov-type convergence theorem and three-series theorem for AANA random variables are established. By using these convergence theorems, we obtain convergence results for AANA sequences, which extend the corresponding ones for independent sequences and NA sequences. In addition, we study the strong stability for weighted sums of AANA random variables and obtain some new results, which extend some earlier ones for NA random variables.

MSC:

60F15 Strong limit theorems
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