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Parameter estimation in uncertain delay differential equations via the method of moments

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  • Gao, Yin
  • Gao, Jinwu
  • Yang, Xiangfeng

Abstract

Uncertain delay differential equations model time-delayed automatic control systems in which noises are described by Liu process. Parameter estimation plays a pivotal part in the applications of uncertain delay differential equations. In this paper, we first obtain a difference equation of uncertain delay differential equations by the forward Euler’s method. A function of the parameter is given by the difference equation, which is verified to obey the standard normal uncertainty distribution. By using the method of moments, we employ the observed data to obtain the empirical moments that equal the moments given by the standard normal uncertainty distribution, the estimated value of parameters are derived. Moreover, some examples are investigated to demonstrate that the method of moments is effective. Finally, we provide an uncertain delay logistic model to describe the population dynamics of American by using the method of parameter estimation proposed in this paper.

Suggested Citation

  • Gao, Yin & Gao, Jinwu & Yang, Xiangfeng, 2022. "Parameter estimation in uncertain delay differential equations via the method of moments," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    • Handle: RePEc:eee:apmaco:v:431:y:2022:i:c:s009630032200385x
    DOI: 10.1016/j.amc.2022.127311
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    References listed on IDEAS

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    1. Jia, Lifen & Sheng, Yuhong, 2019. "Stability in distribution for uncertain delay differential equation," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 49-56.
    2. Guanzhong Ma & Xiangfeng Yang & Xiao Yao, 2021. "A relation between moments of Liu process and Bernoulli numbers," Fuzzy Optimization and Decision Making, Springer, vol. 20(2), pages 261-272, June.
    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. Xiao Wang & Yufu Ning, 2019. "A New Stability Analysis of Uncertain Delay Differential Equations," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-8, January.
    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.
    6. Salvatore Federico, 2011. "A stochastic control problem with delay arising in a pension fund model," Finance and Stochastics, Springer, vol. 15(3), pages 421-459, September.
    Full references (including those not matched with items on IDEAS)

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