Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014, Special Issue (2013), Article ID 179506, 7 pages.
Law of Large Numbers under Choquet Expectations
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.
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 179506, 7 pages.
First available in Project Euclid: 6 October 2014
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Chen, Jing. Law of Large Numbers under Choquet Expectations. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 179506, 7 pages. doi:10.1155/2014/179506. https://projecteuclid.org/euclid.aaa/1412606758