Laws of large numbers of negatively correlated random variables for capacities

Article

DOI: 10.1007/s10255-011-0102-x

Cite this article as:
Li, W. & Chen, Z. Acta Math. Appl. Sin. Engl. Ser. (2011) 27: 749. doi:10.1007/s10255-011-0102-x

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.

Keywords

law of large numbers 2-alternating capacity negatively correlated random variables upper probability 

2000 MR Subject Classification

28C15 

Copyright information

© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina