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Parameter estimation in uncertain differential equations

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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.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61873329), and the University of Chinese Academy of Sciences.

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Authors and Affiliations

  1. School of Economics and Management, University of Chinese Academy of Sciences, Beijing, 100190, China

    Kai Yao

  2. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

    Baoding Liu

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  1. Kai Yao
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  2. Baoding Liu
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Correspondence to Kai Yao.

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Yao, K., Liu, B. Parameter estimation in uncertain differential equations. Fuzzy Optim Decis Making 19, 1–12 (2020). https://doi.org/10.1007/s10700-019-09310-y

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