Laws of large numbers of negatively correlated random variables for capacities

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.

Law of Large Numbers under Choquet Expectations

“…Later, Chen [11] derived a natural extension of the classical Kolmogorov strong LLN to the subadditive case and the related application was given by Chen et al [12]. In 2011, using Chebyshev's inequality and Borel-Cantelli lemma for capacities, Li and Chen [13] provided the LLN for negatively correlated random variables. In 2013, Z. Chen and J. Chen [14] proposed a new proof of maximal distribution theorem and then derived the LLN under sublinear expectations with applications in finance.…”