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Multi-dimensional uncertain differential equation: existence and uniqueness of solution

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Abstract

Multi-dimensional uncertain differential equation is a system of uncertain differential equations driven by a multi-dimensional Liu process. This paper first gives the analytic solutions of two special types of multi-dimensional uncertain differential equations. After that, it proves that the multi-dimensional uncertain differential equation has a unique solution provided that its coefficients satisfy the Lipschitz condition and the linear growth condition.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 71171191 and 71272177), and National Social Science Foundation of China (Grant No. 13CGL057).

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Authors and Affiliations

  1. School of Business, Renmin University of China, Beijing, 100872, China

    Xiaoyu Ji

  2. School of Management, Shanghai University, Shanghai, 200444, China

    Jian Zhou

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  1. Xiaoyu Ji
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  2. Jian Zhou
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Correspondence to Jian Zhou.

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Ji, X., Zhou, J. Multi-dimensional uncertain differential equation: existence and uniqueness of solution. Fuzzy Optim Decis Making 14, 477–491 (2015). https://doi.org/10.1007/s10700-015-9210-z

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  • DOI: https://doi.org/10.1007/s10700-015-9210-z

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