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Moment estimation for parameters in high-order uncertain differential equations

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  • Liu, Zhe
  • Yang, Ying

Abstract

As a type of differential equations with high-order derivatives of uncertain processes, high-order uncertain differential equations are widely applied to modelling dynamic systems in uncertain environment, which usually involve unknown parameters to be estimated. Since observations are always discrete in practice, based on these discrete observations of solution processes, we propose moment estimations for unknown parameters by Euler method approximation of high-order uncertain differential equations. Matching sample moments with corresponding population moments, a system of equations whose solution is the moment estimation of the set of unknown parameters is derived. Finally, some examples illustrate our method in detail.

Suggested Citation

  • Liu, Zhe & Yang, Ying, 2022. "Moment estimation for parameters in high-order uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004738
    DOI: 10.1016/j.amc.2022.127399
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    References listed on IDEAS

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    1. Yang, Xiangfeng & Ralescu, Dan A., 2015. "Adams method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 993-1003.
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    4. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    5. Liu, Z. & Yang, Y., 2021. "Selection of uncertain differential equations using cross validation," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    6. Zhe Liu & Ying Yang, 2020. "Least absolute deviations estimation for uncertain regression with imprecise observations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 33-52, March.
    7. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    8. Zhang, Yi & Gao, Jinwu & Huang, Zhiyong, 2017. "Hamming method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 331-341.
    9. Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
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    Cited by:

    1. He, Liu & Zhu, Yuanguo, 2024. "Nonparametric estimation for uncertain fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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