Abstract
AbstractIn this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.
Funder
Natural Science Foundation of Shandong Province
National Natural Science Foundation of China
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Reference13 articles.
1. Augustin, T.: Optimal decisions under complex uncertainty—basic notions and a general algorithm for data-based decision making with partial prior knowledge described by interval probability. Z. Angew. Math. Mech. 84(10–11), 678–687 (2004)
2. Chen, J.: Law of large numbers under Choquet expectations. In: Abstract and Applied Analysis, vol. 2014. Hindawi (2014)
3. Choquet, G.: Theory of capacities. In: Annales de L’institut Fourier, vol. 5, pp. 131–295 (1954)
4. Doob, J.: Classical Potential Theory and Its Probabilistic Counterpart. Springer, Berlin (1984)
5. Maccheroni, F., Marinacci, M., et al.: A strong law of large numbers for capacities. Ann. Probab. 33(3), 1171–1178 (2005)
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献