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Laws of large numbers of negatively correlated random variables for capacities. (English) Zbl 1260.28012
Summary: Our aim is to present some limit theorems for capacities. We consider a sequence of pairwise negatively correlated random variables. We obtain laws of large numbers for upper probabilities and 2-alternating capacities, using some results in classical probability theory and a non-additive version of Chebyshev’s inequality and a Borel-Cantelli lemma for capacities.
MSC:
28C15Set functions and measures on topological spaces
28A12Contents, measures, outer measures, capacities
60F05Central limit and other weak theorems
60F15Strong limit theorems
91A44Games involving topology or set theory
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References:
[1] Choquet, G. Theory of capacities. Ann. Inst. Fourier, 5: 131--295 (1954) · Zbl 0064.35101 · doi:10.5802/aif.53
[2] Chung, K. A course in probability theory. Academic Press, New York, 1974 · Zbl 0345.60003
[3] Dennerberg, D. Non-additive measure and intergral. Kluwer, Dordrecht, 1994
[4] Ellsberg, Daniel. Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75(4): 643--669 (1961) · Zbl 1280.91045 · doi:10.2307/1884324
[5] Huber, P. J., Strassen, V. Minimax tests and the Neyman-Pearson lemma for capacities. Ann. Statist., 1: 251--263 (1973) · Zbl 0259.62008 · doi:10.1214/aos/1176342363
[6] Marinacci, M. Limit laws for non-additive parobabilities and their frequentist interpretation. J. Econom. theory, 84: 145--195 (1999) · Zbl 0921.90005 · doi:10.1006/jeth.1998.2479
[7] Marinacci, M., Maccheroni, F. A strong law of large numbers for capacities. Ann. Probab., 33: 1171--1178 (2005) · Zbl 1074.60041 · doi:10.1214/009117904000001062
[8] Marinacci, M., Montrucchio, L. Introduction to the mathematics of ambiguity. Working paper series, no.34/2003, 2003 · Zbl 1061.91002
[9] Peng, S. G-Brownian motion and dynamic risk measure under volatility uncertainty. Lectures in CSFI, Osaka University, 2007
[10] Rébillé, Y. Law of large numbers for non-additive measures, 2008. In Artiv: 0801.0984v1 [math.PR].
[11] Schmeidler, D. Integral representation without additivity. Proceedings of the American Society, 97: 255--261 (1986) · Zbl 0687.28008 · doi:10.1090/S0002-9939-1986-0835875-8
[12] Shapley, L. Cores of convex games. Internat. J. Game Theory, 1: 11--26 (1971) · Zbl 0222.90054 · doi:10.1007/BF01753431
[13] Wasserman, L.A., Kadane, J. Bayes’ theorem for capacities. Ann. Statist., 18: 1328--1339 (1990) · Zbl 0736.62026 · doi:10.1214/aos/1176347752