Kybernetika 50 no. 5, 804-813, 2014

On an exponential inequality and a strong law of large numbers for monotone measures

Hamzeh Agahi and Radko MesiarDOI: 10.14736/kyb-2014-5-0804

Abstract:

An exponential inequality for Choquet expectation is discussed. We also obtain a strong law of large numbers based on Choquet expectation. The main results of this paper improve some previous results obtained by many researchers.

Keywords:

Choquet expectation, monotone probability, exponential inequality, a strong law of large numbers

Classification:

60E15, 28A12

paper.pdf

References:

  1. G. Choquet: Theory of capacities. Ann. Inst. Fourier 5 (1954), 131-295.   CrossRef
  2. D. Denneberg: Non-additive Measure and Integral. Kluwer Academic Publishers, Dordrecht 1994.   CrossRef
  3. A. Dvoretzky: On the strong stability of a sequence of events. Ann. Math. Statist. 20 (1949), 2, 296-299.   CrossRef
  4. T. S. Kim and H. C. Kim: On the exponential inequality for negatively dependent sequence. Korean Math. Soc. Commun. 22 (2007), 2, 315-321.   CrossRef
  5. E. Lehmann: Some concepts of dependence. Ann. Math. Statist. 37 (1966), 1137-1153.   CrossRef
  6. J. Li, M. Yasuda, Q. Jiang, H. Suzuki, Z. Wang and G. J. Klir: Convergence of sequence of measurable functions on fuzzy measure spaces. Fuzzy Sets and Systems 87 (1997), 317-323.   CrossRef
  7. R. Mesiar, J. Li and E. Pap: The Choquet integral as Lebesgue integral and related inequalities. Kybernetika 46 (2010), 1098-1107.   CrossRef
  8. H. J. Nooghabi and H. A. Azarnoosh: Exponential inequality for negatively associated random variables. Statist. Papers 50 (2009), 419-428.   CrossRef
  9. P. D. Oliveira: An exponential inequality for associated variables. Statist. Probab. Lett. 73 (2005), 189-197.   CrossRef
  10. E. Pap: Null-additive Set Functions. Kluwer, Dordrecht 1995.   CrossRef
  11. V. V. Petrov: Sums of Independent Random Variables. Springer-Verlag, Berlin 1975.   CrossRef
  12. S. Varošanec: On h-convexity. J. Math. Anal. Appl. 326 (2007), 303-311.   CrossRef
  13. X. Wang, S. Hu, A. Shen. and W. Yang: An exponential inequality for a NOD sequence and a strong law of large numbers. Appl. Math. Lett. 24 (2011), 219-223.   CrossRef
  14. Z. Wang and G. J. Klir: Generalized Measure Theory. Springer, New York 2009.   CrossRef
  15. G. Xing and S. Yang: An exponential inequality for strictly stationary and negatively associated random variables. Commun. Statistics-Theory and Methods 39 (2010), 340-349.   CrossRef
  16. G. D. Xing, S. C. Yang, A. L. Liu and X. P. Wang: A remark on the exponential inequality for negatively associated random variables. J. Korean Statist. Soc. 38 (2009), 53-57.   CrossRef