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The Convergence Theorems of Set-Valued Pramart in a Banach Space

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Nonlinear Mathematics for Uncertainty and its Applications

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

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Abstract

Martingale theory plays an important role in probability theory and applications such as mathematical finance, system control and so on. Classical martingale theory has been extended to more general cases, i.e. the theory of set-valued martingales and fuzzy set-valued martingales. In this paper, we shall introduce the concept of set-valued asymptotic martingale in probability (pramart for short) in a Banach space and discuss its some properties. Then we shall prove two convergence theorems of set-valued pramart in the sense of ∆ and Hausdorff metric in probability respectively.

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Authors and Affiliations

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

    Li Guan & Shoumei Li

Authors
  1. Li Guan
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  2. Shoumei Li
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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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Guan, L., Li, S. (2011). The Convergence Theorems of Set-Valued Pramart in a Banach Space. 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_16

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

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