A note on the cluster set of the law of the iterated logarithm under sub-linear expectations

Li-Xin Zhang

doi:10.3934/puqr.2022006

Article Contents

2022, Volume 7, Issue 2: 85-100. Doi: 10.3934/puqr.2022006

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A note on the cluster set of the law of the iterated logarithm under sub-linear expectations

Li-Xin Zhang

1.
School of Mathematical Sciences, Zhejiang University, Hangzhou 310027, Zhejiang, China

Author Bio: Email: stazlx@zju.edu.cn

Received: February 19, 2022

Accepted: April 17, 2022

Early access: May 2022

Published: June 2022

This work was supported by the NSF of China (Grant Nos. 11731012 and 12031005), Ten Thousands Talents Plan of Zhejiang Province (Grant No. 2018R52042), NSF of Zhejiang Province (Grant No. LZ21A010002), and the Fundamental Research Funds for the Central Universities.

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Abstract

In this note, we establish a compact law of the iterated logarithm under the upper capacity for independent and identically distributed random variables in a sub-linear expectation space. For showing the result, a self-normalized law of the iterated logarithm is established.

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Mathematics Subject Classification: 60F15, 60F05.

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References

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