General laws of large numbers under sublinear expectations |
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| Authors: | Feng Hu Zengjing Chen |
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| Institution: | 1. School of Statistics, Qufu Normal University, Qufu, Shandong, China;2. School of Mathematics, Shandong University, Jinan, Shandong, Chinahufengqf@163.com;4. School of Mathematics, Shandong University, Jinan, Shandong, China;5. Department of Financial Engineering, Ajou University, Yeongtong-gu, Suwon, Korea |
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| Abstract: | ABSTRACTIn this paper, under some weaker conditions, we give three laws of large numbers (LLNs) under sublinear expectations (capacities), which extend the LLN under sublinear expectations in Peng (2008b Peng, S. (2008b). A new central limit theorem under sublinear expectations. arXiv:0803.2656v1 math.PR], 18 Mar 2008. Google Scholar]) and the strong LLN for capacities in Chen (2010 Chen, Z. (2010). Strong laws of large numbers for capacities. arXiv:1006.0749v1 math.PR], 3 Jun 2010. Google Scholar]). It turns out that these theorems are natural extensions of the classical strong (weak) LLNs to the case where probability measures are no longer additive. |
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| Keywords: | Capacity Law of large numbers Maximal distribution Sublinear expectation |
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