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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 179506, 7 pages
http://dx.doi.org/10.1155/2014/179506
Research Article

Law of Large Numbers under Choquet Expectations

School of Mathematics, Shandong University, Jinan 250100, China

Received 13 December 2013; Accepted 13 January 2014; Published 2 March 2014

Academic Editor: Litan Yan

Copyright © 2014 Jing Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

With a new notion of independence of random variables, we establish the nonadditive version of weak law of large numbers (LLN) for the independent and identically distributed (IID) random variables under Choquet expectations induced by 2-alternating capacities. Moreover, we weaken the moment assumptions to the first absolute moment and characterize the approximate distributions of random variables as well. Naturally, our theorem can be viewed as an extension of the classical LLN to the case where the probability is no longer additive.