Chinese Annals of Mathematics, Series B

, Volume 40, Issue 1, pp 39–54 | Cite as

Convergences of Random Variables Under Sublinear Expectations

  • Zechun Hu
  • Qianqian Zhou


In this note, the authors survey the existing convergence results for random variables under sublinear expectations, and prove some new results. Concretely, under the assumption that the sublinear expectation has the monotone continuity property, the authors prove that convergence in capacity is stronger than convergence in distribution, and give some equivalent characterizations of convergence in distribution. In addition, they give a dominated convergence theorem under sublinear expectations, which may have its own interest.


Sublinear expectation Capacity The dominated convergence theorem 

2000 MR Subject Classification

60J45 60G51 


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The authors thank the anonymous referee for providing helpful suggestions and comments to improve and clarify the manuscript.


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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of MathematicsSichuan UniversityChengduChina
  2. 2.School of Mathematical SciencesNankai UniversityTianjinChina

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