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Set-Valued Square Integrable Martingales and Stochastic Integral

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Combining Soft Computing and Statistical Methods in Data Analysis

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 77))

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Abstract

In this paper, we firstly introduce the concept of set-valued square integrable martingales. Secondly, we give the definition of stochastic integral of a stochastic process with respect to a set-valued square integrable martingale, and then prove the representation theorem of this kind of integral processes. Finally, we show that the stochastic integral process is a set-valued sub-martingale.

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Authors and Affiliations

  1. Department of Applied Mathematics, Beijing University of Technology, Beijing, 100124, P.R. China

    Shoumei Li

Authors
  1. Shoumei Li
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Editor information

Editors and Affiliations

  1. Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing Edificio Científico-Tecnológico. 3a Planta, C/ Gonzalo Gutiérrez Quirós s/n, 33600, Mieres, Spain

    Christian Borgelt , Gil González-Rodríguez  & Wolfgang Trutschnig ,  & 

  2. Departamento de Estadística e I.O. y D.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Asunción Lubiano

  3. Departamento de Estadística e I.O. yD.M., Universidad de Oviedo, Facultad de Ciencias, C/ Calvo Sotelo s/n, 33007, Oviedo, Spain

    María Ángeles Gil

  4. Systems Research Institute, Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Przemysław Grzegorzewski

  5. Systems Research Institute, Polish Academy of Science, Newelska 6, 01-447, Warsaw, Poland

    Olgierd Hryniewicz

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Li, S. (2010). Set-Valued Square Integrable Martingales and Stochastic Integral. In: Borgelt, C., et al. Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing, vol 77. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14746-3_51

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  • DOI: https://doi.org/10.1007/978-3-642-14746-3_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14745-6

  • Online ISBN: 978-3-642-14746-3

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