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Nonlinear Mathematics for Uncertainty and its Applications pp 19–30Cite as

Strong Laws of Large Numbers for Bernoulli Experiments under Ambiguity

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

In this paper, we investigate the strong laws of large numbers on upper probability space which contains the case of Bernoulli experiments under ambiguity. Our results are natural extensions of the classical Kolmogorov’s strong law of large numbers to the case where probability measures become to imprecise. Finally, an important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.

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References

  1. Chen, Z.: Strong laws of large numbers for capacities. arXiv: 1006.0749v1 (math.PR) (June 3, 2010)

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Author information

Authors and Affiliations

  1. Department of Mathematics, Shandong University, Jinan, China

    Zengjing Chen & Panyu Wu

  2. Department of Financial Engineering, Ajou University, Suwon, Korea

    Zengjing Chen

Authors
  1. Zengjing Chen
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  2. Panyu Wu
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Chen, Z., Wu, P. (2011). Strong Laws of Large Numbers for Bernoulli Experiments under Ambiguity. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_2

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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