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Strong Law of Large Numbers under an Upper Probability
Graduate Department of Financial Engineering, Ajou University, Suwon, South Korea
- 1 Graduate Department of Financial Engineering, Ajou University, Suwon, South Korea
Applied Mathematics·Volume 03 (2012)·Pages 2056–2062·Published 28 December 2012·DOI10.4236/am.2012.312A284
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Abstract
Strong law of large numbers is a fundamental theory in probability and statistics. When the measure tool is nonadditive, this law is very different from additive case. In 2010 Chen investigated the strong law of large numbers under upper probabilityVby assumingVis continuous. This assumption is very strong. Upper probabilities may not be continuous. In this paper we prove the strong law of large numbers for an upper probability without the continuity assumption whereby random variables are quasi-continuous and the upper probability is generated by a weakly compact family of probabilities on a complete and separable metric sample space.
KeywordsStrong Law of Large NumbersUpper ProbabilityWeakly CompactIndependenceQuasi-Continuous
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