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Moment estimation in uncertain differential equations based on the Milstein scheme

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  • Tang, Han
  • Yang, Xiangfeng

Abstract

Difference schemes are needed for approximating uncertain differential equations in applications. This paper mainly derives a new difference scheme called the Milstein scheme. It is theoretically shown that the Milstein scheme is superior to the previous Euler scheme. Then the Milstein scheme is applied to the method of moments so that the estimated uncertain differential equation fits the observations better. Moreover, the bias function is introduced to assess the precision of the estimation method. Finally, some numerical examples are given to verify the performance of both schemes and minimum cover estimation.

Suggested Citation

  • Tang, Han & Yang, Xiangfeng, 2022. "Moment estimation in uncertain differential equations based on the Milstein scheme," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009085
    DOI: 10.1016/j.amc.2021.126825
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    References listed on IDEAS

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    1. 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.
    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.
    6. Tang, Han & Yang, Xiangfeng, 2021. "Uncertain chemical reaction equation," Applied Mathematics and Computation, Elsevier, vol. 411(C).
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