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Estimating time-varying parameters in uncertain differential equations

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  • Zhang, Guidong
  • Sheng, Yuhong

Abstract

Research on the estimation of unknown parameters in uncertain differential equations has been a concerned subject for scholars in recent years. For this reason, some scholars have proposed many methods to estimate the unknown parameters. However, these unknown parameters are constants. This paper considers estimation methods for time-varying parameters, the least squares estimation method is rewritten. Firstly, estimates of a set of time-varying parameters are obtained. Secondly, the fit function for this set of estimates, which is obtained by means of a regression fit is considered to be a time-varying parameter. Meanwhile, the criteria is given to determine whether the fit function is reasonable. Finally, two numerical examples of uncertain differential equations are presented to verify the feasibility of the above method.

Suggested Citation

  • Zhang, Guidong & Sheng, Yuhong, 2022. "Estimating time-varying parameters in uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    • Handle: RePEc:eee:apmaco:v:425:y:2022:i:c:s0096300322001680
    DOI: 10.1016/j.amc.2022.127084
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    References listed on IDEAS

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    1. Waichon Lio & Baoding Liu, 2021. "Initial value estimation of uncertain differential equations and zero-day of COVID-19 spread in China," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 177-188, June.
    2. Liu, Z., 2021. "Generalized moment estimation for uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. 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).
    4. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    5. 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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