The laws of large numbers for Pareto-type random variables under sub-linear expectation

Abstract

In this paper, some laws of large numbers are established for random variables that satisfy the Pareto distribution, so that the relevant conclusions in the traditional probability space are extended to the sub-linear expectation space. Based on the Pareto distribution, we obtain the weak law of large numbers and strong law of large numbers of the weighted sum of some independent random variable sequences.

Key words： Sub-linear expectation; Pareto type distribution; laws of large numbers; independent and identical distribution

Acknowledgments

The authors thank the National Natural Science Foundation of China (Grant No. 12061028), Guangxi Natural Science Foundation Joint Incubation Project (Grant No. 2018GXNSFAA294131), Guangxi Natural Science Foundation (Grant No. 2018GXNSFAA281011), and Innovation Project of Guangxi Graduate Education (Grant No. YCSW2020175) for their financial support. The authors sincerely thank the editors and anonymous reviewers for their valuable comments.

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