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Parameter estimation in uncertain differential equations

Author

Listed:
  • Kai Yao

    (University of Chinese Academy of Sciences)

  • Baoding Liu

    (Tsinghua University)

Abstract

Parameter estimation is a critical problem in the wide applications of uncertain differential equations. The method of moments is employed for the first time as an approach for estimating the parameters in uncertain differential equations. Based on the difference form of an uncertain differential equation, a function of the parameters is proved to follow a standard normal uncertainty distribution. Setting the empirical moments of the functions of the parameters and the observed data equal to the moments of the standard normal uncertainty distribution, a system of equations about the parameters is obtained whose solutions are the estimates of the parameters. Analytic examples and numerical examples are given to illustrate the proposed method of moments.

Suggested Citation

  • Kai Yao & Baoding Liu, 2020. "Parameter estimation in uncertain differential equations," Fuzzy Optimization and Decision Making, Springer, vol. 19(1), pages 1-12, March.
    • Handle: RePEc:spr:fuzodm:v:19:y:2020:i:1:d:10.1007_s10700-019-09310-y
    DOI: 10.1007/s10700-019-09310-y
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    References listed on IDEAS

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    4. Gao, Rong, 2016. "Milne method for solving uncertain differential equations," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 774-785.
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