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Chinese Annals of Mathematics, Series B

, Volume 39, Issue 5, pp 791–804 | Cite as

Strong Laws of Large Numbers for Sublinear Expectation under Controlled 1st Moment Condition

  • Cheng Hu
Article

Abstract

This paper deals with strong laws of large numbers for sublinear expectation under controlled 1st moment condition. For a sequence of independent random variables, the author obtains a strong law of large numbers under conditions that there is a control random variable whose 1st moment for sublinear expectation is finite. By discussing the relation between sublinear expectation and Choquet expectation, for a sequence of i.i.d random variables, the author illustrates that only the finiteness of uniform 1st moment for sublinear expectation cannot ensure the validity of the strong law of large numbers which in turn reveals that our result does make sense.

Keywords

Sublinear expectation Strong law of large numbers Independence Identical distribution Choquet expectation 

2000 MR Subject Classification

60F15 

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsShandong Normal UniversityJinanChina

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