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Laws of large numbers of negatively correlated random variables for capacities

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Abstract

Our aim is to present some limit theorems for capacities. We consider a sequence of pairwise negatively correlated random variables. We obtain laws of large numbers for upper probabilities and 2-alternating capacities, using some results in the classical probability theory and a non-additive version of Chebyshev’s inequality and Boral-Contelli lemma for capacities.

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Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Wen-juan Li & Zeng-jing Chen

Authors
  1. Wen-juan Li
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  2. Zeng-jing Chen
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Corresponding author

Correspondence to Wen-juan Li.

Additional information

Supported by the National Basic Research Program of China (973 Program, No. 2007CB814901).

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Li, Wj., Chen, Zj. Laws of large numbers of negatively correlated random variables for capacities. Acta Math. Appl. Sin. Engl. Ser. 27, 749–760 (2011). https://doi.org/10.1007/s10255-011-0102-x

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  • DOI: https://doi.org/10.1007/s10255-011-0102-x

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