Laws of large numbers for infinite means with mixing sequences

Jian Han, Xiaoqin Li, Yudan Cheng


In this paper, we consider the laws of large numbers with infinite means based on $\varphi$-mixing sequences. An exact weak law and a strong law are obtained for $\varphi$-mixing asymmetrical Cauchy random variables. It is also presented that the weak law cannot extend to a strong law. In addition, some simulations are presented to illustrate our results of the laws of large numbers.


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