, Volume 27, Issue 4, pp 749-760
Date: 09 Sep 2011

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.

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