Convergences of Random Variables Under Sublinear Expectations
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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.
KeywordsSublinear expectation Capacity The dominated convergence theorem
2000 MR Subject Classification60J45 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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