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Synergies of Soft Computing and Statistics for Intelligent Data Analysis pp 93–101Cite as

On Equations with a Fuzzy Stochastic Integral with Respect to Semimartingales

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 190))

Abstract

We consider some equations in a metric space of fuzzy sets with basis of square integrable random vectors. These equations generalize the single-valued stochastic differential equations and set-valued stochastic integral equations as well. A main object is a fuzzy stochastic trajectory integral with respect to a semimartingale. We obtain the existence and uniqueness of global solutions to fuzzy stochastic integral equations driven by continuous semimartingales. Also, we present a stability of solutions under changes of equation’s data.

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Author information

Authors and Affiliations

  1. Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, 65-516, Zielona Góra, Poland

    Marek T. Malinowski

Authors
  1. Marek T. Malinowski
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Correspondence to Marek T. Malinowski .

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Editors and Affiliations

  1. Faculty of Computer Science, Otto-von-Guericke University of Magdebur, Geb. 29, Raum 008, Universitätsplatz 2, Magdeburg, 39106, Germany

    Rudolf Kruse

  2. , FB Informatik & Informationswissenschaft, University of Konstanz, Konstanz, 78457, Germany

    Michael R. Berthold

  3. of Magdeburg, Faculty of Computer Science, Otto-von-Guericke University, Geb. 29, Universitätsplatz 2 008, Magdeburg, 39106, Germany

    Christian Moewes

  4. , Department of Statistics and OR, University of Oviedo, C/ Calvo Sotelo, s/n, Oviedo, 33007, Spain

    María Ángeles Gil

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

    Przemysław Grzegorzewski

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

    Olgierd Hryniewicz

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Malinowski, M.T. (2013). On Equations with a Fuzzy Stochastic Integral with Respect to Semimartingales. In: Kruse, R., Berthold, M., Moewes, C., Gil, M., Grzegorzewski, P., Hryniewicz, O. (eds) Synergies of Soft Computing and Statistics for Intelligent Data Analysis. Advances in Intelligent Systems and Computing, vol 190. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33042-1_11

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  • DOI: https://doi.org/10.1007/978-3-642-33042-1_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33041-4

  • Online ISBN: 978-3-642-33042-1

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