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Stability in mean for multi-dimensional uncertain differential equation

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Abstract

Liu process is an uncertain process with stationary and independent increments. Multi-dimensional uncertain differential equation is a type of differential equation driven by multi-dimensional Liu process to model a multi-dimensional dynamic system. This paper aims at proposing a definition of stability in mean for multi-dimensional uncertain differential equations. Then a stability theorem for a multi-dimensional uncertain differential equation being stable in mean is proved. Furthermore, some examples are given to show what is stable in mean.

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Acknowledgements

This work was supported in part by Wild Goose Pagoda Scholar Project of Xi’an University of Finance and Economics.

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Authors and Affiliations

  1. Science and Technology on Information Systems Engineering Laboratory, College of Information System and Management, National University of Defense Technology, Changsha, 410000, China

    Yanghe Feng & Guangquan Cheng

  2. Department of Statistics, Xi’an University of Finance and Economics, Xi’an, 710061, China

    Xiaohu Yang

Authors
  1. Yanghe Feng
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  2. Xiaohu Yang
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  3. Guangquan Cheng
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Correspondence to Xiaohu Yang.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by Y. Ni.

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Feng, Y., Yang, X. & Cheng, G. Stability in mean for multi-dimensional uncertain differential equation. Soft Comput 22, 5783–5789 (2018). https://doi.org/10.1007/s00500-017-2659-7

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  • DOI: https://doi.org/10.1007/s00500-017-2659-7

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