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Strong and weak convergence for asymptotically almost negatively associated random variables. (English) Zbl 1269.60036
Summary: The strong law of large numbers for sequences of asymptotically almost negatively associated (AANA) random variables is obtained, which generalizes and improves the corresponding one by Z. D. Bai and P. E. Cheng [Stat. Probab. Lett. 46, No. 2, 105–112 (2000; Zbl 0960.60026)] for independent and identically distributed random variables. In addition, the Feller-type weak law of large numbers for sequences of AANA random variables is obtained, which generalizes the corresponding one by W. Feller [Am. J. Math. 68, 257–262 (1946; Zbl 0060.28704)] for independent and identically distributed random variables.
MSC:
60F15Strong limit theorems
60F05Central limit and other weak theorems